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Prudent valuation

Marco Bianchetti
May 10, 2016
520

Prudent valuation

Traditionally, quantitative finance practitioners are divided into two populations: those who seek fair values, i.e. means of price distributions, and those who seek risk measures, i.e. quantiles of price distributions. Fair value people and risk people typically live in separate lands, and worship different gods: the profit and loss balance sheet, and regulatory capital, respectively.

Prudent Valuation is a rather unexplored midland which has recently emerged somewhere in between the well known mainlands of Pricing and Risk Management. In fact, the Capital Requirements Regulation (CRR), requires financial institutions to apply prudent valuation to all fair value positions. The difference between the prudent value and the fair value, called Additional Valuation Adjustment (AVA), is directly deducted from the Core Equity Tier 1 (CET1) capital. The Regulatory Technical Standards (RTS) for prudent valuation proposed by the EBA have been adopted by the EU (reg. 2016/101) on 28th Jan. 2016.

The 90% confidence level required by regulators for prudent valuation links quantiles of price distributions (exit prices) to capital, thus bridging the gap between the Pricing and Risk Management mainlands, and forcing the crossbreeding of the fair value and risk populations above.

In this seminar, we will explore the Prudent Valuation land.

Marco Bianchetti

May 10, 2016
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  1. Prudent Valuation Here we go Global Derivatives Trading & Risk

    Management Budapest, 10 May 2016 Marco Bianchetti Head of Fair Value Policy, Financial and Market Risk Management, Intesa Sanpaolo Adjunct Professor, University of Bologna In collaboration with Umberto Cherubini – Professor of Mathematical Finance, Bologna University AIFIRM – Association of Italian Financial Risk Managers
  2. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 2 Summary [1] 1. Introduction o Overview o Prudent valuation history 2. Theoretical Background o Price opacity & financial crisis o Pricing beyond Black-Scholes o Market incompleteness & illiquidity 3. Regulation o Overview o The Capital Requirement Regulation 575/2013 o The EBA Regulatory Technical Standards o AVAs vs XVAs o Prudent valuation reporting o Prudent valuation data NEW NEW
  3. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 3 Summary [2] 4. AVA calculation o Definitions and basic assumptions o Market price uncertainty AVA o Close-out costs AVA o Model risk AVA o Unearned credit spreads AVA o Investing and funding costs AVA o Concentrated positions AVA o Future administrative costs AVA o Early termination AVA o Operational risk AVA 5. Prudent valuation framework o Implementation o Methodological framework o Operational framework o IT framework o Documentation & reporting o Example of prudent valuation framework 6. Conclusions 7. References 8. Glossary NEW
  4. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 4 1: Introduction Overview Traditionally, quantitative finance practitioners are divided into two populations: those who seek fair values, i.e. means of price distributions, and those who seek risk measures, i.e. quantiles of price distributions. Fair value people and risk people typically live in separate lands, and worship different gods: the profit and loss balance sheet, and regulatory capital, respectively. Prudent Valuation is a rather unexplored midland which has recently emerged somewhere in between the well known mainlands of Pricing and Risk Management. In fact, the Capital Requirements Regulation (CRR), requires financial institutions to apply prudent valuation to all fair value positions. The difference between the prudent value and the fair value, called Additional Valuation Adjustment (AVA), is directly deducted from the Core Equity Tier 1 (CET1) capital. The Regulatory Technical Standards (RTS) for prudent valuation proposed by the EBA have been adopted by the EU (reg. 2016/101) on 28th Jan. 2016. The 90% confidence level required by regulators for prudent valuation links quantiles of price distributions (exit prices) to capital, thus bridging the gap between the Pricing and Risk Management mainlands, and forcing the crossbreeding of the fair value and risk populations above. In this seminar, we will explore the Prudent Valuation land.
  5. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 5 1: Introduction Overview Q-Land Q-measure Pricing: extrapolate the present Fair value Profit and loss P-Land P-measure Risk: model the future Risk measures Capital Prudent Land Prudent measure Price distribution 90% exit price Capital
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    10 May 2016 p. 6 See A. Meucci, “P versus Q: Differences and Commonalities between the Two Areas of Quantitative Finance”, GARP Risk Professional, pp. 47-50, February 2011, http://ssrn.com/abstract=1717163 1: Introduction P vs Q and beyond
  7. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 7 The idea of prudent valuation dates back to Basel 2 regulation (see BCBS, “International Convergence of Capital Measurement and Capital Standards – A revised framework”, June 2004). In particular, sec. VI (“Trading book issues”), ch. B (“Prudent valuation guidance”), par. 690-701 set the requirements for prudent valuation in terms of o systems and controls, o valuation methodologies, o valuation adjustments or reserves, impacting regulatory capital (not P&L). The CRR inherited most of the contents in its art. 105. In more recent times, prudent valuation has been required by the Financial Stability Agency (FSA) to UK institutions, see refs. below. o Financial Services Authority, “Dear CEO Letter: Valuation and Product Control”, August 2008, http://www.fsa.gov.uk/pubs/ceo/valuation.pdf o Financial Services Authority, “Product Control Findings and Prudent Valuation Presentation”, November 2010, http://www.fsa.gov.uk/pubs/other/pcfindings.pdf o Financial Services Authority, “Regulatory Prudent Valuation Return”, Policy Statement 12/7, April 2012, http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml 1: Introduction Prudent valuation history [1/3]
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    10 May 2016 p. 8 1: Introduction Prudent valuation history [2/3] August 2008 FSA “Dear CEO letter” November 2010 FSA “Product Control Findings and Prudent Valuation Presentation” April 2012 FSA “Regulatory Prudent Valuation Return”, Policy Statement 2008 2009 2010 2011 2012 2006 2007 2004 2005 June 2004 BCBS “International Convergence of Capital Measurement and Capital Standards” (Basel 2)
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    10 May 2016 p. 9 1: Introduction Prudent valuation history [3/3] 13 November 2012 EBA Discussion Paper (EBA/DP/2012/03) 10 July 2013 EBA Consultation Paper (EBA/CP/2013/28) 1 Jan. 2014 CRR 575/2013 31 March 2014 EBA Final Draft RTS and first application of prudent valuation 28 Jan. 2016 EBA RTS published on OJEU 8 November 2013 EBA Quantitative Impact Study 2012 2013 2014 2015 23 Jan. 2015 EBA Final Draft RTS amended Prudent valuation in place 2016 28 October 2015 EU commission adoption of EBA RTS NEW
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    10 May 2016 p. 10 Elaborated by AIFIRM Market Risk Committee, working group on prudent valuation, 148 pages, publicy available at http://www.aifirm.it/position- paper-prudent-valuation Summary  Executive summary  Introduction  Regulatory requirements  Prudent Valuation scope  General assumptions and considerations  Theoretical background  AVA calculation under the simplified approach  AVA calculation under the core approach  Prudent valuation operating framework  Prudent valuation technology  Conclusions  Appendixes  References  Glossary and notation 1: Introduction Prudent valuation guidelines and sound practices NEW
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    10 May 2016 p. 11 Summary 2. Theoretical background o Price opacity & financial crisis o Pricing beyond Black-Scholes o Market incompleteness & illiquidity
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    10 May 2016 p. 12 o Price opacity & financial crisis the crisis, and the Enron case before, has introduced the problem of valuation as a mean of diffusion of losses among financial institutions and assets. o Pricing beyond Black-Scholes the problem of getting the price wrong is linked to the fact that, already after the 19th October1987 market crash, the standard Black-Scholes assumptions of normal distribution of assets returns and perfect replication in continuous time of all financial products proved wrong. o Market incompleteness & illiquidity other sources of risk, not traded in the market, such as volatility and correlation (smile and skew) have surfaced as key valutation elements. The hedging problem has become more complex and perfect hedging impossible (the market incompleteness problem). Moreover, if hedging can be done (volatility swaps or correlation swaps), it has to be done in highly illiquid markets, or even with OTC transactions. o Credit risk: “unearned credit spreads”, that is expected loss due to default of the counterparty has become the major element in the evaluation of a financial product. This has added even more focus on hedging complexities. 2: Theoretical background Introduction
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    10 May 2016 p. 13 2: Theoretical background A history of financial crises  September-October, 1998 LTCM, the major issue of the crisis is the impossibility to replicate financial derivatives in continuous time, and in perfectly liquid markets. It is the first case of incomplete markets.  December, 2001 Enron, the issue is lack of transparency in accounting data. The impact was uncertainty of valuation of similar companies or companies with the same auditor (Arthur Andersen). It was called “financial contagion by incomplete information”.  May 2005 Sudden drop in credit correlation triggered losses in financial intermediaries absorbing equity risk in securitization deals. It was a case about correlation uncertainty and hedging risk. Equity hedging strategies based on mezzanine were turned into losses by a major decrease in correlation.  2007-2008 Subprime crisis. The crisis themes were illiquidity, lack of transparency and an increase in correlation (systemic risk). On top of that, the peculiar issue of the crisis was the role played by the accounting standards in spreading contagion across intermediaries.
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    10 May 2016 p. 14 2: Theoretical background Accounting and the subprime crisis What is the link between financial crisis and valuation?  “Default losses on US subprime mortgages about 500 billion dollars.  But in a mark-to-market world, deadly losses are valuation losses o Valuation losses as high as 4 trillions. o Major banks failed without a single penny of default  BIS study of rescue package: 5 trillions in committed resources. “ Eli Remolona, IV Annual Risk Management Conference, Singapore, July 2010
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    10 May 2016 p. 15 2: Theoretical background Toxic assets .  “Financial assets the value of which has fallen significantly and may fall further, especially as the market for them has frozen. This may be due to hidden risks within the assets becoming visible or due to changes in extremal market environment” FT Lexicon  Toxic assets are a matter of: o Liquidity (“market frozen”) o Opacity and ambiguity (“hidden risks becoming visible”) o “Extremal market environment”
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    10 May 2016 p. 16 2: Theoretical background A simple example [1]  Take a very simple financial product, that is an equity linked note promising to pay a participation to the increase in some stock market index in five years.  The replicating portfolio of the product is made up by: o A zero coupon bond paying the Libor with five years maturity o A zero coupon bond paying the credit risk spread of the issuer with five years maturity o An equity option with five years exercise time  The main sources of valuation uncertainty are the following. o The calibration of the five year zero coupon Libor, using fixed income market data and bootstrapping techniques. This valuation problem is common to other fixed income products. o The calibration of the five year zero coupon credit spread, using the issuer’s or comparable CDS and bond data, and bootstrapping techniques. o The calibration of the five year equity volatility, using equity options’ market data and bootstrapping techniques. Typically, exchange traded or OTC derivatives do not have a liquid market for 5 years maturity and we must extend implied volatility beyond the traded maturities.
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    10 May 2016 p. 17 2: Theoretical background A simple example [2]  There are actually other risk sources, mostly the correlations among the risk factors involved. o Correlation between equity and bonds It could seem that this should not affect the pricing problem, since it is made under the Forward Martingale Measure (FMM), but the volatility of the forward price depends on correlation. o Correlation between underlying asset and volatility This is relevant in cases in which the underlying asset and its volatility co-move in directions leading to a decrease of the embedded option. This is not the case of this product, which is long both in the underlying asset and its volatility, while the equity market and volatility are known to be negatively correlated. o Correlation between the embedded option and the credit quality of the issuer Actually the embedded option is a vulnerable option whose value is affected by the positive correlation between the exposure (the exercise of the option) and the default probability of the issuer.
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    10 May 2016 p. 18 2: Theoretical background Incomplete markets: definition  Complete markets are defined by all financial products being “attainable”. This means that the payoff of every financial contract or product can be exactly replicated by some trading strategy. This implies lack of frictions and continuous rebalancing of the replicating portfolio. Markets are assumed to be perfectly liquid and trading is costless.  If markets are complete, there exists a unique Equivalent Martingale Measure (EMM) such that the price of each and every asset can be computed by the expected value under such measure, and discounted with the risk-free rate. With complete markets the price of each financial product would be unique, and there would be no valuation uncertainty problem.  Real world markets are incomplete and there exists a valuation uncertainty problem. The reason is that no perfect hedge exists. More precisely, the reasons for incomplete markets are: o there are not enough assets to hedge all possible risk factors (no enough Arrow- Debreu prices); o replicating portfolios cannot be rebalanced in continuous time in such a way as to allow for a perfect hedge; o there is not enough liquidity in the market, particularly in stress times, to allow rebalancing of the replicating portfolios.
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    10 May 2016 p. 19 2: Theoretical background Incomplete markets: theory  From a technical point of view, selecting a price in incomplete markets amounts to choose a probability measure (pricing kernel) in a set of probability measures. This set  contains the probabilities such that the price of each product is a martingale. This implies that for each product it is not possible to find a replicating strategy that attains the product for sure. = (, )()ȁ ∈ ℘  The problem is then to define:  the set of probabilities  including all the risk-neutral probabilities;  a strategy to select a probability in the set.  Notice that the problem of selecting a probability amounts to selecting a lottery. So, a possible strategy to select a specific probability is to use expected utility or some of its extensions.  Hedging error: every probability measure that is chosen is subjected to hedging error. Based on this, for example, one could select the probability with the lowest hedging variance, in the set with some expected hedging cost.
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    10 May 2016 p. 20 2: Theoretical background Incomplete markets: back to expected utility  We remind that expected utility ranks lotteries by the expected value of a function of the pay-off. The function weighting the pay-off is increasing and concave (for risk- averse decision makers) and is called utility function. So, lottery A is preferred to lottery B if E(U(A)) > E(U(B)) with U(x) the utility function.  Ellsberg paradox: what happens if the probability of some lottery is not known for sure? If there is a preference for the lottery whose probability is known, or for the other, the expected utility does not work.  Example: there are 90 balls in an urn, we know that 30 are Red, and the others are Blue or Green. Do you have any preference between:  A lottery paying a premium if the ball is Red  A lottery paying a premium if the ball is Blue  Now consider the choice between:  A lottery paying a premium if the ball is Blue or Green  A lottery paying a premium if the ball is Red or Green  If you have preferences of Red over Blue, then Prob(Red) = 1/3 > Prob(Blue), by consistently: Prob(Red  Green) < Prob(Blue  Green) = 2/3 and Prob(Blue) > 1/3
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    10 May 2016 p. 21 2: Theoretical background Incomplete markets: non-additive expected utility  Notice that the problem with expected utility is additivity. In fact, since additivity means Prob(A  B) = P(A) + P(B), for A and B disjoint, we have Probl(Red) + Prob (Green) > Prob(Blue) + Prob(Green) which implies Prob(Red) > Prob(Blue).  This implies that allowing for the preferences in the two lotteries to be represented by the same measure one has to break down additivity.  Non additive representations of preferences are called capacities. These measures are monotone and are not required to be additive. The expected value with respect to capacities is represented by the Choquet integral.  There is a duality relationship between sub and super additive capacities and between lower and upper Choquet integrals. The duality reminds of the Dempster- Shafer theory.  We will see that this representation is important to represent the set of probability measures.
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    10 May 2016 p. 22 2: Theoretical background Alternative theories for price bounds  There are two different approaches to address valuation uncertainty. In both cases the price bounds are obtained by assuming interval valuation.  Uncertain Volatility Model  Volatility is assumed be included in a given interval  This leads to two conservative pricing bounds (BSB PDE functions)  Avellaneda, Levy and Paràs (1996), AMF  Choquet pricing  Interval probabilities (MMEU, Gilboa and Schmeidler, 1989)  Conservative valuation (Choquet integral)  Cherubini (1997) AMF, Cherubini and Della Lunga (2001) AMF AMF = Applied Mathematical Finance  MMEU: assume the worst possible probability scenario and select the choice that yields the maximum expected utility.
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    10 May 2016 p. 23 2: Theoretical background Uncertain Volatility Model  Set the delta-neutral portfolio  Volatility choice  The Black-Scholes formula becomes non linear (Black-Scholes-Baremblatt) where arg min ≤≤ 1 2 22 2 2 = , 2 2 > 0, , 2 2 < 0. min ≤≤ Π = + 1 2 22 2 2 = Π = − . 2 2 2 + : = 2 , 2 2 > 0, 2 , 2 2 < 0. + 1 2 2 2 2 + 2 2 2 + − = 0,
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    10 May 2016 p. 24 2: Theoretical background Choquet pricing  Long and short positions  Long and short positions are represented by Choquet integrals with respect to capacities.  Given a function f and a non-additive measure , the upper and lower Choquet integrals are defined as = min ∈℘ න , , , long position, max ∈℘ න , , , short position. න −∞ 0 ≤ + න 0 +∞ 1 − ≤ , lower Choquet integral, න −∞ 0 1 − ≥ + න 0 +∞ ≥ upper Choquet integral.
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    10 May 2016 p. 25 2: Theoretical background Choquet pricing  Assume the Breeden and Litzenberger representation of the pricing kernel and the corresponding call and put prices. According to Breeden and Litzenberger the probability of exercise of an option can be recovered from the derivative of the option with respect to the strike price.  By integrating the pricing kernel we can then recover the prices of call and put options as a function of the integral of cumulative distributions, that is, as Choquet integrals, − 1 , = > , ⇒ = (, ) න +∞ ) 1 − ( , 1 , = ≤ ⇒ = (, ) න −∞ () .
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    10 May 2016 p. 26 2: Theoretical background Examples of valuation uncertainty  Derivatives with counterparty risk CVA and DVA with correlation between the underlying asset and the credit risk of the counterparty (wrong way risk)  Toxic assets Example: a senior tranche, with high attachment, of a securitization deal traded on the market at much lower value.  Correlation products that is Breeden and Litzenberger representation of the pricing kernel and the corresponding call and put prices. Example: options on baskets.  Illiquid derivatives with concentration risk Large derivative positions require large positions of the underlying asset for delta hedging. Example: large plain vanilla calls/puts on funds.
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    10 May 2016 p. 27 2: Theoretical background CVA valuation  Assume that the payment schedule of a swap be {t1 , t2 ,…, tn } and that default of the counterparty receiving fixed rate (B) occurred between tj-1 and tj . In this case the loss suffered by the surviving counterparty A will be where sr is the swap rate at the date of default and k is that at the origin.  By the same token, the loss suffered by B due to default of A will be           1 - n j i 1 A 0 , , max , Lgd n j i t t sr k t t P           1 - n j i 1 B 0 , , max , Lgd k t t sr t t P n j i
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    10 May 2016 p. 28 2: Theoretical background CVA valuation with copula function  Denote GB (tj ) the survival probability of party B beyond time tj . Then, the default probability between time tj - 1 and time tj is GB (tj-1 ) – GB (tj ). Moreover, assume C(u,v) to be a copula function, and Q(x) the pricing kernel of the swap rate  Then the CVA for counterparty A will be                    1 1 1 , 1 , n j i K j B j B i B d t G t G Q C t t P Lgd  
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    10 May 2016 p. 29 2: Theoretical background CVA valuation with wrong way risk  Now assume perfect dependence between the underlying asset and default of the counterparty. In this case, we have the Fréchet bound , ≤ ; . In this case, the CVA can be computed in closed form as CVA = LgdB max[k*(tj ) – k,0]A(t, tj , tn) [GB (tj-1 ) – GB (tj )] – LgdB PayerSwaption(.;max(k*(tj ),k)) where k*(tj ) is defined from Q((sr(tj ,tn ) > k*(tj )) = GB (tj-1 ) – GB (tj ), and is the swap annuity. (; , ) = ෍ = −1 , −1
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    10 May 2016 p. 30 2: Theoretical background CVA valuation with wrong way risk o For the short end of the contract the worst scenario is perfect negative dependence between the underlying asset and default of the counter party. In this case, we have the Fréchet bound , > + − 1; 0 . In this case, the CVA can be computed in closed form as CVA = LgdA [ReceiverSwaption(.;min(k*(tj ),k)) – Receiver swaption(.;k)] + LGDA max[k – k*(tj ),0](1 – GA (tj – 1 ) – GA (tj ))
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    10 May 2016 p. 31 2: Theoretical background CVA valuation with wrong way risk (long party) Vulnerable Call Swaptions: Financial Institution Paying Fixed 0 0,002 0,004 0,006 0,008 0,01 0,012 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Independence Perfect positive dependence
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    10 May 2016 p. 32 2: Theoretical background CVA valuation with wrong way risk (short party) Vulnerable Put Swaptions: Financial Institution Receiving Fixed 0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 0,004 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Independence Perfect Negative Dependence
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    10 May 2016 p. 33 2: Theoretical background Tranche senior  Assume a senior tranche with attachment equal to 30%, so that it begins to absorb losses only from 30% of collateral on.  Assume a standard valuation model such as Vasicek asymptotic model, that is based on the assumption that all exposures in the basket have the same default probability P and the same asset correlation  with systemic risk.  Then, the expected loss of a senior tranche with attachment is = − −1 , −1 , 1 − 2 where −1 , −1 , is the Gaussian copula function.  Now notice that by considering the two extreme values of the copula function , = and , = min(, ) yields extreme values for the expected losses of the senior tranche.
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    10 May 2016 p. 34 2: Theoretical background Tranche senior: pricing bounds 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 Rho = 0 Rho = 1
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    10 May 2016 p. 35 2: Theoretical background Rainbow options  Assume a call option on the minimum of a set of assets (Everest). This can be priced with a Choquet integral using the copula as the Choquet integral  From the point of view of the issuer, we can compute the conservative value in closed form, for a bivariate product         d T S Q T S Q T S Q C T t P T K S S S Call K N N      ) ) ( ( ),... ) ( ( ), ) ( ( , ) , ), ,... , (min( 2 1 2 1                 ) *, max( ; , ; , * ; , , , 2 1 1 * *] , max[ 2 * 1 1 * 2 K K t S C K t S C K t S C d S Q T t P d S Q T t P C K K K K K K K K               1 1    
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    10 May 2016 p. 36 2: Theoretical background Dynamic replication of illiquid derivatives  Now assume you are trading a derivative with a costumer, maybe for a large quantity of the underlying asset (concentration risk) or for an illiquid underlying. In this case, standard textbook references for the pricing of options do not apply, since the production process of the derivative has an impact on the underlying asset.  Here the only process is to start with a dynamics of the underlying asset and to try a replication strategy, allowing for the liquidity cost of rebalancing the portfolio, and the funding cost of changing the leverage position. So, the market price incorporates liquidity costs, both in the sens of market liquidity and funding liquidity. Both the sources of cost are all the more relevant the larger the size of the position.  The problem of finding an optimal trade-off between liquidity cost and liquidity risk is extremely involved. In fact, it requires to define trading strategies: how many times to rebalance, when, whether at fixed intervals or contingent on some rule.  The problem is magnified by the need to specify the market impact function, that includes:  Which is the trade off between the market impact due to sudden rebalance trades versus the volatility risk to which one is exposed for partitioned unwinding  How much of the market impact is temporary and how much is permanent. Permanent impacts make the problem particularly involved.
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    10 May 2016 p. 37 Summary 3. Regulation o Overview o The Capital Requirement Regulation 575/2013 o The EBA Regulatory Technical Standards o AVAs vs XVAs o Prudent valuation reporting o Prudent valuation data
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    10 May 2016 p. 38 3: Regulation Overview  Articles 34 and 105 of Capital Requirements Regulation (CRR, n. 575/2013), in force since 1 January 2014, require financial institutions to apply prudent valuation to all fair value positions (included positions outside the trading book), setting a new prudential requisite for regulatory capital including valuation uncertainty.  The difference between the prudent value and the fair value, accounted in the institution’s balance sheet, is called “Additional Valuation Adjustment” (AVA), and is directly deducted from the Core Equity Tier 1 (CET1) capital.  Following the CRR, the EBA published a Discussion Paper (EBA/DP/2012/03), a Consultation Paper (EBA/CP/2013/28), and a Final Draft (EBA/RTS/2014/06), to be approved by the EU Commission, setting the Regulatory Technical Standards (RTS) for prudent valuation.  The EBA Final Draft defines the AVA calculation methodology using two alternative approaches, named Simplified Approach and Core Approach. The Final Draft sets also the requirements on systems, controls and documentation that should support the prudent valuation process.  Acronyms: CRR, AVA, CET1, EBA, RTS, EU,  Keywords: fair/prudent value, simplified/core approach
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    10 May 2016 p. 39 Market Data Models Estim ates Fair Value accounting AVA (Additional Valuation Adjustment) IFRS 13 Prudent valuation Prudent value Deducted from Common Equity Tier 1 capital CRR article 105 requisites Policies & procedures Control systems Prudent valuation principles 3: Regulation CRR 575/2013 [1/8]
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    10 May 2016 p. 40 3: Regulation CRR 575/2013 [2/8] Art. 34 Prudent valuation scope Systems and controls Valuation Valuation adjustments Art. 105 CRR 575/2013 CRR Prudent Valuation Tree Prudent valuation principles Degree of certainty, art. 105.1 S&C requirements, art. 105.2 Revaluation frequency art. 105.3 Mark to market, art. 105.4-5 Mark to model, art. 105.6-7 IPV, art. 105.8 Valuation adjustments, art. 105.9-10 Illiquid positions, art. 105.11 Other valuation adj., art. 105.12 Complex products, art. 105.13
  41. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 41  CRR art. 34: scope and target o Scope: all assets measured at fair value o Target: CET1 capital (not P&L) 3: Regulation CRR 575/2013 [3/8]
  42. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 42  CRR art. 105.1, scope and degree of certainty: all positions are subject to prudent valuation, achieving an appropriate degree of certainty with regard to: o the dynamic nature of the positions, o the demands of prudential soundness, and o the mode of operation and purpose of capital requirements in respect of trading book positions.  CRR art 105.2, systems and controls: institutions establish and maintain systems and controls to ensure prudent and reliable valuations, including at least. o Documented policies and procedures for the valuation process, including: • clearly defined responsibilities of the various areas involved in the determination of the valuation, • sources of market information and review of their reliability, • guidelines for the use of unobservable inputs that reflect the assumptions of authority on the elements used by market participants to determine the price of the position, • frequency of independent valuation, • timing of closing prices, • procedures for the correction of assessments, • procedures for the reconciliation of month end and ad hoc. o Clear and independent (of the front office) reporting lines for the department in charge of the valuation process. 3: Regulation CRR 575/2013 [4/8]
  43. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 43  CRR art 105.3, revaluation frequency: institutions revalue trading book positions at least daily  CRR art 105.4-5, mark to market: institutions mark their positions to market whenever possible, using the more prudent side of bid and offer unless they can close out at mid market.  CRR art 105.6, mark to model: where marking to market is not possible, institutions must conservatively mark to model their positions and portfolios. 3: Regulation CRR 575/2013 [5/8]
  44. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 44  CRR art 105.7, mark to model: o senior management must be aware of the fair-valued positions marked to model and must understand the materiality of the uncertainty of the risk/performance of the business; o source market inputs, where possible, in line with market prices, and assess the appropriateness of market inputs and model parameters on a frequent basis; o use valuation methodologies which are accepted market practice; o where the model is developed by the institution itself, it must be based on appropriate assumptions, assessed and challenged by suitably qualified parties independent of the development process; o have in place formal change control procedures, hold a secure copy of the model and use it periodically to check valuations; o risk management must be aware of the weaknesses of the models used and how best to reflect those in the valuation output; o models are subject to periodic review to determine the accuracy of their performance, including assessment of the continued appropriateness of assumptions, analysis of profit and loss versus risk factors, and comparison of actual close out values to model outputs; o the model must be developed or approved independently of the trading desk and independently tested, including validation of the mathematics, assumptions and software implementation. 3: Regulation CRR 575/2013 [6/8] Very detailed article regarding valuation in general
  45. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 45  CRR art. 105.8, independent price verification (IPV): institutions perform independent price verification in addition to daily marking to market/model. Verification of market prices and model inputs must be performed by unit independent from units that benefit from the trading book, at least monthly, or more frequently depending on the nature of the market or trading activity. Where independent pricing sources are not available or pricing sources are more subjective, prudent measures such as valuation adjustments may be appropriate.  CRR art 105.9-10: valuation adjustments: institutions establish and maintain procedures for considering valuation adjustments, and formally consider the following: unearned credit spreads, close-out costs, operational risks, market price uncertainty, early termination, investing and funding costs, future administrative costs and, where relevant, model risk.  CRR art 105.11, illiquid/concentrated positions: Institutions shall establish and maintain procedures for calculating an adjustment to the current valuation of any less liquid positions, which can in particular arise from market events or institution-related situations such as concentrated positions and/or positions for which the originally intended holding period has been exceeded. 3: Regulation CRR 575/2013 [7/8]
  46. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 46  CRR art. 105.12, other valuation adjustments: institutions must consider whether to apply a valuation adjustment also: o when using third party valuations, o when marking to model, o for less liquid positions, including an ongoing basis review their continued suitability, o for uncertainty of parameter inputs used by models.  CRR art. 105.13, complex products: institutions must explicitly assess the need for valuation adjustments to reflect the model risk associated with using: o a possibly incorrect valuation methodology o unobservable (and possibly incorrect) calibration parameters in the valuation model. 3: Regulation CRR 575/2013 [8/8]
  47. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 47 3: Regulation Fair Value Vs Prudent Value [1] Fair Value o Regulation: IFRS13 o Application: balance sheet o Percentile: 50% (expected value) o The price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date o Must include all the factors that a market participants would use, acting in their economic best interest. o Atoms: single trades. o Fair value adjustments o Non-entity specific Prudent value o Regulation: CRR/EBA o Application: CET1 o Percentile: 90% o Must reflect the exit price at which the institution can trade within the capital calculation time horizon. o Atoms: valuation positions subject to a specific source of price unertainty o Entity specific o Subject to diversification benefit (50% weight for MPU, CoCo, MoRi AVAs)
  48. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 48 3: Regulation Fair Value Vs Prudent Value [2] Why capital and not P&L ?  P&L is accounted under accounting standards o EU listed companies: use IFRS (International Financial Reporting Standards), established and maintained by the IASB (International Accounting Standards Board) see www.ifrs.org o US listed companies: use GAAP (Generally Accepted Accounting Standards), established and maintained by the FASB (Financial Accounting Standards Board), see www.fasb.org o Convergence towards IFRS is in progress  Both IFRS and GAAP define the fair value as an exit price, not as a prudent price. Fair value must be fair, not prudent.  Thus, regulators have decided to account for prudent price through capital, instead of altering the accounting standards.
  49. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 49 3: Regulation Overlaps and possible offsets AVAs have to be deducted by CET1. Hence, possible double counting w.r.t. other capital deductions should be considered.  AVA UCS vs Expected Loss Amounts CRR article 159 states that “Institutions shall subtract the expected loss amounts calculated in accordance with Article 158 (5), (6) and (10) from the general and specific credit risk adjustments and additional value adjustments in accordance with Articles 34 and 110 and other own funds reductions related to these exposures…”. The Credit Risk capital requirements, including the expected loss (EL) amount, are calculated using the higher accounting values, not the AVA adjusted values. As a result, without an adjustment to the capital requirements on those assets, there is a double hit to capital. The AVA UCS offset against EL, in Article 159, is a mitigation that prevents from double hit.  Day One Profit & Loss deductions Since these are deductions from profit and loss to account for fair value uncertainty, it seems that there exist a double counting with AVAs, and AVAs can be reduced accordingly. See survey.  Others To be understood and clarified, possibly with regulators.
  50. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 50 3: Regulation EBA RTS: overview  The EBA RTS issued on 23rd Jan. 2015 have been adopted by the EU with Commission delegated regulation (EU) 2016/101, published on the OJEU on  The RTS set the detailed regulatory technical standards on prudent valuation under articles 34 and 105 of CRR  The most important feature of the EBA RTS is the distinction between two different approaches for the implementation of the prudent valuation methodology: the simplified approach and the core approach.  The choice between the two approaches depends on a threshold on the sum of the absolute values of fair-valued assets and liabilities. The EBA sets the threshold at EUR 15 billion.  The EBA RTS sets further requirements in terms of documentation (art. 18), systems and controls (art. 19). These provisions essentially require Institutions to have in place a two-level internal policy for fair value (Fair Value Policy) and for prudent value (Prudent Valuation Policy).
  51. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 51 3: Regulation EBA RTS: overview General provisions Sec. 1 Core approach Sec.3 EBA RTS Final draft EBA RTS Prudent Valuation Tree Simplified approach Sec.2 Documentation systems & controls Sec.4 Methodology for AVA, art. 1 Definitions, art. 2 Sources of market data, art. 3 Conditions of application, art. 4 AVA calculation, art. 5 AVA aggregation, art. 6 Overview, fall back, art. 7 General provisions, art. 8 AVA calculation, art. 9-17 Documentation, art. 18 Systems & controls, art. 19 Entry into force, art. 20 AVA OpR, art. 17 AVA EaT, art. 16 AVA FAC, art. 15 AVA CoPo, art. 14 AVA IFC, art. 13 AVA UCS, art. 12 AVA MoRi, art. 11 AVA CoCo, art. 10 AVA MPU, art. 9
  52. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 52 3: Regulation EBA RTS: prudent valuation scope [1/9] General rules  Region of application: since the CRR is an EU directive, prudent valuation applies to all institutions within EU countries. In case of institution made of a central holding and one or more subsidiaries, prudent valuation applies to those individual subsidiaries included in EU countries.  Scope of application: the CRR art. 5, defines the prudent valuation scope as including all trading book positions. However, the CRR art. 34 requires that institutions apply the standards of art. 105 to all assets measured at fair value. The combination of the above CRR articles 34 and 105 implies that the prudent valuation scope includes all fair-valued positions, regardless of whether they are held in the trading book or banking book. The positions at fair value held in both trading and banking books are the following: Assets Liabilities Financial assets held for trading (HFT) Financial liabilities held for trading (HFT) Financial assets at fair value Financial liabilities at fair value Financial assets available for sale (AFS) (for the portion not subject to prudential filters)
  53. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 53 3: Regulation EBA RTS: prudent valuation scope [2/9]  Positions excluded: o the EBA RTS, art. 4.2 and 8.1, allow Institutions to exclude partially or totally from the prudent valuation scope those positions for which a change in their accounting fair value has only a partial or zero impact on Common Equity Tier 1 capital. These positions must be included in proportion to the impact of the relevant valuation change on CET1 capital. o In particular these positions are the following: 1. positions subject to prudential filters, 2. exactly matching, offsetting positions (back to back), 3. positions in hedge accounting. o Notice that, since the size of the positions above may be relevant, the prudent valuation scope is the primary driver of the AVA figures. o How to compute inclusion/exclusion in practice ? See next slides.
  54. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 54 3: Regulation EBA RTS: prudent valuation scope [3/9] 1. Positions subject to prudential filers o Positions subject to prudential filters refer to the "Financial assets available for sale" (AFS). The inclusion/exclusion of these positions from the prudent valuation scope of application follows the CRR requirements. o The exact percentages of partial inclusions follows the transitional provisions that each local Regulator issued in compliance with the above CRR requirements. o Partial inclusion means, for instance, that if 40% of fair value gains and losses are filtered in CET1, the residual 60% of fair value gains and losses are included in the prudent valuation scope. In case of 100% filter, the position is completely excluded by prudent valuation. Position under prudential filters (AFS) Inclusion Government bonds issued by EU countries 0% Other debt securities (excluding the EU government bonds above) Partial inclusion depending on the sign of the reserve and on local prescriptions Equity Partial inclusion depending on the sign of the reserve and on local prescriptions
  55. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 55 Transitional provisions issued by national regulators. 3: Regulation EBA RTS: prudent valuation scope [4/9] Circolare 285 Banca d’Italia The applicable percentage following art. 467, par. 3 CRR is: a) 20% since 1 Jan. 2014 to 31 Dec. 2014 b) 40% since 1 Jan. 2015 to 31 Dec. 2015 c) 60% since 1 Jan. 2016 to 31 Dec. 2016 d) 80% since 1 Jan. 2017 to 31 Dec. 2017 Local regulation in Italy Article 467 CRR […] institutions shall include in the calculation of their Common Equity Tier 1 items only the applicable percentage
  56. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 56 3: Regulation EBA RTS: prudent valuation scope [5/9] Institutions may not include in own funds unrealized gains and losses related to AFS positions with central administrations. Circolare 285 Banca d’Italia The applicable percentage following art. 468, par. 3 CRR is: a) 100% 1 Jan. 2014 to 31 Dec. 2014 b) 60% since 1 Jan. 2015 to 31 Dec. 2015 c) 40% since 1 Jan. 2016 to 31 Dec. 2016 d) 20% since 1 Jan. 2017 to 31 Dec. 2017 Article 468 CRR […] institutions shall remove in the calculation of their Common Equity Tier 1 items only the applicable percentage Local regulation in Italy
  57. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 57 3: Regulation EBA RTS: prudent valuation scope [6/9] According to Regulation (EU) 2016/445 of the European Central Bank of 14 Mar 2016 (published OJEU on 26 Mar. 2016), art. 14 and 15, the corresponding art. 467 and 468 of CRR (setting prudential filters for AFS positions) are modified such that AFS positions in EU government Bonds shall no longer subject to 100% filter, but shall be subject to standard prudential filters holding for other AFS position:  Inclusion of unrealized losses (art. 14 -> art. 467 CRR): o 60% in [1/1/2016 – 31/12/2016] o 80% in [1/1/2017 – 31/12/2017]  Exclusion of unrealized gains (art. 15 -> art. 468 CRR): o 40% in [1/1/2016 – 31/12/2016] o 20% in [1/1/2017 – 31/12/2017]  First application date: Q4-2016 This regulatory change will change substantially the AVA figures for institutions with huge positions in EU govies (more or less all banks...). NEW
  58. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 58 3: Regulation EBA RTS: prudent valuation scope [7/9] 2. Exactly matching, offsetting positions (back to back) o Back to back positions are groups of trades with total null valuation exposure to market risk factors (interest rates, volatility, etc.), since any variation in the relevant market valuation inputs generates opposite variations in the value of the trades in the group, such that the total value is constant. In other words, the group has null total sensitivity to market risk factors. o We stress that back to back positions are neutral w.r.t. other risk factors, such as counterparty defaults, since the trades into the group may be subscribed with different counterparties. o From a prudent valuation point of view: • Simplified approach: 100% exclusion (EBA RTS art. 4.2) • Core approach: AVAs must be calculated based on the proportion of the accounting valuation change that impacts CET1 capital (EBA RTS art. 8.1). In practice: • AVA MPU, CoCo and MoRi are null, • AVA UCS, IFC, CoPo, FAC, EaT, OpR must be computed on the total valuation exposure of the back to back portfolio.
  59. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 59 3: Regulation EBA RTS: prudent valuation scope [8/9] 3. Hedge accounting positions o Hedge accounting positions are characterized by a hedged instrument (e.g. one ore more securities, loans or mortgages, etc.) and an hedging instrument (e.g. one ore more interest rate swaps, credit default swaps, etc.). o The total package of hedged + hedging instruments has, by construction, a reduced sensitivity to the underlying risk factors. o From a prudent valuation point of view, all AVAs must be computed on the total valuation exposure of the hedge accounting portfolio.
  60. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 60 3: Regulation EBA RTS: prudent valuation scope [9/9] Positions subject to prudential filters (AFS) Positions in hedge accounting Positions for which a change in their accounting fair value has only a partial or zero impact on CET 1 Art. 4.2 and 8.1 EBA RTS Prudent Valuation scope: exclusions Positions in back to back EU Gov. bonds Other bonds Equity General criteria for exclusion Positions excluded % of exclusion 100% until Sept. 16 Partial, phase in Partial, phase in Simplified appr. Partial, residual exposure of hedged + hedging items Core appr. 100% Partial, residual exposure to UCS, IFC, CoPo, FAC, EaT, OpR AVAs
  61. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 61 3: Regulation EBA RTS: simplified approach Simplified Approach (EBA RTS, sec. 2)  Institutions may apply the Simplified Approach if the sum of the absolute value of fair-valued assets and liabilities is less than EUR15 bn.  The Simplified Approach AVA is given by the 0,1% of the sum of the absolute value of fair-valued assets and liabilities. Example of AVA calculation under the simplified approach. Data do not refer to real portfolios. Below threshold
  62. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 62 3: Regulation EBA RTS: core approach [1/3] Core Approach (EBA RTS, sec. 3)  Institutions that at individual or consolidated level exceed the EUR15bn threshold must apply the core approach.  Each AVA is the excess of valuation adjustments required to achieve the identified prudent value, over any adjustment applied in the institution’s fair value that can be identified as addressing the same source of valuation uncertainty as the AVA.  Whenever possible, the prudent value of a position is linked to the 90% percentile of its price distribution. In practice for AVAs i) Market price uncertainty ii) Close-out costs iii) Unearned credit spreads, the Institutions must compute the prudent value using the available market data and the 90% target confidence.  Whenever insufficient data exists to construct a plausible range of values, institutions shall use an expert-based approach using qualitative and quantitative information available to achieve a 90% level of certainty in the prudent value. Additional Valuation Adjustments
  63. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 63 3: Regulation EBA RTS: core approach [2/3] Core approach Additional Valuation Adjustments Market Price Uncertainty (MPU) Art. 9 Close Out Costs (CoCo) Art. 10 Model Risk (MoRi) Art. 11 Unearned Credit Spread (UCS) Art. 12 Investing & Funding Cost (IFC) Art. 13 Concen- trated Positions (CoPo) Art. 14 Future Admin Costs (FAC) Art. 15 Early Termination (EaT) Art. 16 Main AVAs UCS/IFC AVAs Other AVAs Operational Risk (OpR) Art. 17 The AVA hierarchy Market risk factors 50% weights for diversification Market risk factors Split onto main AVAs Non-market risk factors 100% weights, no diversification
  64. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 64 3: Regulation EBA RTS: core approach [3/3] Example of AVA calculation and aggregation under the core approach. IFC and UCS AVAs are split into their MPU, CoCo and MoRi components and pre-aggregated to the corresponding AVAs, then the total AVA is obtained from the aggregation of the other seven residual AVAs. In order to show toy but realistic figures, we assumed the principal AVAs equal to 1/7 of the 99% x 0.1% of the total FV under the core approach. AVA OpR has been calculated as for a non-AMA Institution. In the last line, we also add a possible AVA fall-back calculated on the remaining 1% x 0.1% of the total FV. Above threshold
  65. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 65 3: Regulation EBA RTS: fall-back approach [1/2] Fall back approach (EBA RTS, art. 7.2.b) Institutions that exceed the EUR15bn threshold but cannot calculate the core approach AVAs for certain positions, are allowed to apply a «fall-back approach» (actualy very capital intensive), and compute AVAs for those positions as the sum of:  100% of the net unrealised profit (NUP)  10% of the notional value in case of derivatives;  25% of the absolute difference between the fair value (FV) and the net unrealised profit for non-derivatives. In formulas: "unrealised profit shall mean the change, where positive, in fair value since trade inception, determined on a first-in-first-out basis.” A = 100% + + 10% + 25% − + − +: = ෍ =1 , 0 , = ෍ =1 , = ෍ =1 .
  66. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 66 3: Regulation EBA RTS: fall-back approach [2/2] Example of AVA calculation under the fall-back approach. We assume to apply the Fall-Back approach to the 1% portion of the previous core portfolio. The net unrealized P&Ls are the 0.1% of the fair values, positive for derivatives and negative for bonds. The notional for derivatives is assumed 10 times the fair value. The AVA Fall-Back is then summed to the remaining 99% of the previous AVA core to obtain the total AVA.
  67. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 67  The core approach is mandatory only for institutions above the threshold of €15 bln.  Institutions below the threshold may choose between simplified and core approaches.  Which one is more convenient (generate smaller capital absorption) ? There is no precise mathematical relation between the simplified and core AVAs. The actual figures depend principally on the actual positions included in the prudent valuation scope. 3: Regulation Simplified vs core approaches [1/2]
  68. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 68 3: Regulation Global view of key regulatory concepts Fair value CRR art. 34, 105 EBA RTS Prudent value Scope 90% confidence level Simplified approach Mark to market Mark to model IPV Systems and controls Core approach Expert based Fall back Diversification 0.1% Formula 9 AVAs
  69. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 69 3: Regulation AVAs vs XVAs Simple question, difficult answer Should XVAs be included into the prudent valuations scope ? Let’s look atthe state of the art... ...and try some forecast XVA Accounting standards Accounting practice CVA, DVA YES, both IFRS13 and GAAP mention about counterparty and own credit risk. Some news on DVA expected YES, CVA and DVA are normally included into accounting fair value and reported in public balance sheet disclosures FVA NO, at least not explicitly YES, most banks have included FVA into accounting fair value and report some (scarce) information in public balance sheet disclosures MVA NO, see recent survey NO, see recent survey and public balance sheet disclosures KVA NO, see Kenyon&Kenyon, Risk Mag. Mar. 2016 NO, see recent survey xxxVA Who knows... NEW
  70. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 70 Recently, two regulators proposed a consultation on enhancements to the reporting of prudent valuation figures.  The industry (ISDA, IIF, AFME, etc.) is actively discussing the proposed template and comments to BCBS are expected. Main issues are the following: o Partial overlapping and consistency of AVA definitions under BCBS and EBA RTS o Different AVA scopes of applications, since EBA RTS allows for many exclusions. o AVAs break down by asset class is problematic for EU Institutions because EBA RTS requires AVA calculation at valuation exposure level. For example, AVA MPU for some risk factor (e.g. IR/vols and FX rates/vols) naturally include multiple asset classes. 1. BCBS Consultative Document, “Pillar 3 disclosure requirements – consolidated and enhanced framework”, March 2016, issued for comment by 10 June 2016.  Template PV1, in particular, aims to disclose prudent valuation figures under Pillar 3, consistently with previous BCBS requirements: o BCBS “International Convergence of Capital Measurement and Capital Standards” (Basel 2, comprehensive version) June 2006, paragraphs 698-701. o BCBS “Supervisory guidance for assessing banks’ financial instrument fair value practices”, April 2009 (in particular Principle 10). 3: Regulation Prudent valuation reporting [1/3] NEW
  71. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 71 Template PV1 proposed in BCBS Consultative Document, “Pillar 3 disclosure requirements – consolidated and enhanced framework”, March 2016, issued for comment by 10 June 2016. 3: Regulation Prudent valuation reporting [2/3] NEW
  72. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 72 2. EBA consultation paper (EBA/CP/2016/02), ”Draft implementing Technical Standards amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016, issued for comment by 31 March 2016. The proposed amendement of prudent valuation supervisory reporting is articulated into four new templates.  Template C 32.01: fair valued asset and liabilities o Rows: accounting categorisation (HFT, AFS, etc.) o Columns: fair value amounts of inclusions and exclusions according to EBA RTS  Template C 32.02: core approach o Rows: break down by portfolio/trade class (vanilla/exotic), diversification benefit, fall back app. o Columns: AVAs and fair value adjustments according to EBA RTS.  Template C 32.03: focus on AVA MoRi  Template C 32.01: focus on AVA CoPo Main issues are the following:  breakdown by portfolio/trade class (vanilla/exotic) is not consistent with AVA calculation by valuation exposures,  amount of data required 3: Regulation Prudent valuation reporting [3/3] NEW
  73. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 73 FV under prudent valuation scope = FV asset & liabilities – FV under prudential filters 3: Regulation Prudent valuation data: QIS [1/3]
  74. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 74  The EBA conducted a QIS to estimate the total impact of the requirements of the RTS including 59 banks across 15 jurisdictions, with the following results.  Small banks: < 15 €/bln  Medium banks: 15 - 100 €/bln  Large banks: > 100 €/bln Average 227 €/mln per bank 3: Regulation Prudent valuation data: QIS [2/3]
  75. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 75 According to EBA: [*]  approximately 6,500 credit institutions across EEA Member States (as of 2013) report supervisory data to their respective competent authorities.  Total value of assets: approximately EUR 42,000 billion.  Approximately 750 institutions (11%) are above the EUR 15 billion threshold. [*] European Banking Authority, Consultation Paper, “Draft Implementing Technical Standards amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016, https://www.eba.europa.eu/-/eba-seeks-comments-on-reporting-of-prudent-valuation- information 3: Regulation Prudent valuation data: QIS [3/3]
  76. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 76 3: Regulation Prudent valuation data: 2014-2015 [1/3] Source: elaboration of public data (in collaboration with Ernst Young). NEW
  77. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 77 3: Regulation Prudent valuation data: 2014-2015 [2/3] Source: elaboration of public data (in collaboration with Ernst Young). NEW
  78. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 78 Comments  Fair value is given by FV assets + FV liablities including o Held for trading (HFT) o Fair Value Option (FVO) o Hedging Derivatives (HD) o Available For Sale (AFS)  Fair value for prudent valuation has been estimated from fair value excluding HD and AFS (100%, no AFS filters applied, slightly underestimated).  AVA/CET1 figures are rather different, ranging from negligible to important %.  AVA core / AVA simplified > 1 in a few cases, thus AVA simplified is neither an AVA cap nor an AVA floor.  Prudent valuation not driven by L3 instruments: moving from AVA/L3 to AVA /(L2+L3) changes the figures by a factor of 100.  2014-2015 average AVAs double the 2013 QIS result (500 vs 227 mln€). 3: Regulation Prudent valuation data: 2014-2015 [3/3] NEW
  79. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 79 1. XVAs 3: Regulation Prudent valuation data: survey [1/4]  Restricted access to clients only  Dec.2015  30 respondents (18 GSIBs, 15 UK)  60 questions  EBA RTS not yet in place at the time  One third does not account FVA in fair value, more than half does account AVA IFC in prudent value.  MVA and KVA are not accounted both in fair and prudent values. NEW
  80. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 80 1. XVAs (cont’d) 3: Regulation Prudent valuation data: survey [2/4]  Only 30% use a spread term structure  «Peer estimate» is a possible answer to the question «what is an exit price for FVA ?»  Possible use of Markit XVA service  Both funding spreads sources and term structures vary considerably, both for FVA (Fair Value) and for AVA IFC (prudent value) NEW
  81. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 81 2. P&L variance test 3: Regulation Prudent valuation data: survey [3/4]  The P&L variance test is difficult to run and pass in case of many relevant risk factors, and may lead to huge AVA MPU.  60% ignore the P&Lvariance test  Only 7% run extensive application  Only 14% apply with quarterly frequency NEW
  82. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 82 3. Other 3: Regulation Prudent valuation data: survey [4/4]  One half does apply/does not apply offsetting between AVAs and other regulatory capital reserves.  Possible offsets should be clarified, to avoid possible capital double countings.  One third reduces the valuation exposure. NEW
  83. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 83 4. AVA calculation o Definitions and basic assumptions o Market price uncertainty AVA o Close-out costs AVA o Model risk AVA o Unearned credit spreads AVA o Investing and funding costs AVA o Concentrated positions AVA o Future administrative costs AVA o Early termination AVA o Operational risk AVA o Case studies & examples Summary
  84. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 84 4: AVA calculation Definitions and basic assumptions [1] In other words, a valuation position will display valuation exposures to its valuation inputs. Clearly the degree of valuation exposure to a valuation input depends on the particular valuation position. Definitions (EBA RTS art. 2) Item Definition Example Valuation position A portfolio of financial instruments or commodities measured at fair value, held in both trading and non-trading books E.g. a portfolio of derivatives Valuation input A set of parameters (observable or non- observable) that influences the fair value of a valuation position E.g. yield curve,volatility cube, market/historical correlations, prepayment, etc. Valuation exposure The amount of a valuation position which is sensitive to the change in a valuation input E.g. the trades in portfolio above sensible to the valuation inputs above.
  85. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 85 4: AVA calculation Definitions and basic assumptions [2] Fair value In general, we denote the fair value of a valuation position at time t with , or, shortly, with , with = 1, … , . Given a set of valuation positions subject to prudent valuation, we denote the total fair value as = ෍ =1 In the context of prudent valuation, we consider the following properties of fair value FV.  FV is positive for assets ( > 0) and negative for liabilities ( < 0).  Financial institutions have appropriate internal IPV process in place (EBA RTS, p. 7).  FV is computed by the institution consistently with the applicable financial reporting standards, e.g. IFRS13, and with its internal fair value policy.  The institution possibly applies and reports a number of valuation adjustments to the FV, according to its internal fair value policy.
  86. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 86 4: AVA calculation Definitions and basic assumptions [3] Fair value (cont’d)  The FV of a valuation position may be subject to the sources of uncertainty mentioned in the CRR, art. 105.10-11, and thus associated to a specific AVA under the core approach described in the EBA RTS.  According to EBA RTS art. 8.3, the FV of a valuation position associated to a specific AVA under the core approach must include all the fair value adjustments possibly applied by the institution associated to the same source of valuation uncertainty as the specific AVA. In case a fair value adjustment cannot be associated to the same source of valuation uncertainty of a specific AVA, it must not be included in the FV for the specific AVA calculation. In case of impossible association with any AVA, the fair value adjustment cannot be included at all in the prudent valuations scope.
  87. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 87 4: AVA calculation Definitions and basic assumptions [4] Fair value (cont’d)  Fair value for derivatives In general, we may consider the fair value for derivatives split into various components, = 0 + = + + + + ⋯ where o 0 is the “base” fair value component at valuation time t, as if the contract were covered by a perfect CSA; o the other components gathered in corresponds to the value of the various risk components underlying the financial instrument, such as the bilateral counterparty risk , funding risk , bid-ask , model risk , etc. Such components may be considered or not in the FV or in in according to the fair value policy of the institution.
  88. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 88 4: AVA calculation Definitions and basic assumptions [5] Fair value (cont’d)  Fair value for securities We consider the fair value for securities, instead, as a single value, without splitting into distinct components. In other words, the value of the various risk components is included in the credit spread associated to the security.
  89. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 89 4: AVA calculation Definitions and basic assumptions [6] Valuation input  The FV of a valuation position depends on its valuation inputs, denoted with , = 1, … , ,  The FV may be also denoted as (, , 1 , … , ). We stress that different valuation positions depend, in general, on different valuation inputs.  The valuation input is associated to a single elementary risk factor, or source of valuation uncertainty.
  90. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 90 4: AVA calculation Definitions and basic assumptions [7] Valuation exposure  The valuation exposure of a valuation position to the valuation input is the amount of that valuation position which is sensitive to the change in the valuation input .  The valuation exposure can be also associated to the sensitivity of the valuation position to the valuation input .  In a wider sense, the valuation exposure is anything that measures the dependency of the FV of the valuation position to the valuation input .
  91. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 91 4: AVA calculation Definitions and basic assumptions [8] Prudent value  We denote the prudent value of category k for a valuation position associated to the source of valuation uncertainty at time t with (, , , ) or, shortly, with , with = 1, … , and = 1, … , . The category is the AVA type (MPU, CoCo, etc…).  Degree of certainty The CRR (article 105.1) requires a prudent value that achieves an “… appropriate degree of certainty”. The EBA RTS specifies the appropriate degree of certainty as follows. o AVA MPU, CoCo e MoRi (art. 9-11): • where possible, the prudent value of a position is linked to a range of plausible values and a specified target level of certainty (90%); • in all other cases, an expert-based approach is allowed, using qualitative and quantitative information available to achieve an equivalent level of certainty as above (90%). o AVA UCS and IFC (art. 12-13): these AVAs must be split into their MPU, CoCo and MoRi components, and aggregated to the corresponding MPU, CoCo and MoRi AVAs, respectively. Thus, the same level of certainty in the prudent value (90%) must be statistically achieved.
  92. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 92 4: AVA calculation Definitions and basic assumptions [9] Prudent value (cont’d) o Other AVAs (CoPo, FAC, ET, OpR, art. 14-17): it must be statistically achieved the same level of certainty in the prudent value (90%) as for the previous AVAs (art. 8.3). o For positions where there is valuation uncertainty but it is not possible to statistically achieve a specified level of certainty, the same target degree of certainty in the prudent value (90%) is required. o “The EBA accepts that for the majority of positions where there is valuation uncertainty, it is not possible to statistically achieve a specified level of certainty; however, specifying a target level is believed to be the most appropriate way to achieve greater consistency in the interpretation of a “prudent’ value”.” In conclusion, the same degree of certainty in the prudent value (90%) must be achieved for all AVAs.
  93. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 93 4: AVA calculation Definitions and basic assumptions [10] Prudent value (cont’d) o Notice that, by definition, the prudent value is always equal to or lower than the fair value, both for assets and liabilities. Taking into account the FV definition above we have, for both assets and liabilities, ≤ ∀ = 1, … , , = 1, … , , = 1, … , o Hence, PV is generally positive for assets ( > 0) and negative for liabilities ( < 0). This is not strictly true in all cases, since some asset (e.g. an OTC swap) may have positive FV and negative PV (not viceversa).
  94. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 94 4: AVA calculation Definitions and basic assumptions [11] Additional Valuation Adjustment (AVA)  Simplified approach Given the total fair value of assets and liabilities, > 0, < 0, the total AVA under the simplified approach is given by the following expression = 0.1% × + where ≔ ෍ =1 , ≔ ෍ =1 .
  95. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 95 4: AVA calculation Definitions and basic assumptions [12] Additional Valuation Adjustment (AVA) (cont’d)  Core approach Given the fair value of a valuation position , , and the corresponding prudent value of category k associated to the source of valuation uncertainty , , the AVA under the core approach is given by the following expressions , , , : = , − , , , , , : = ෍ =1 ෍ =1 , , , , where: o is the aggregation weight, such that = 0.5,0.5,0.5,1,1,1,1 for the seven AVAs MPU, CoCo, MoRi, CoPo, FAC, ET, OpR, respectively. o ≔ , , , is the k-th AVA for valuation position and source of valuation uncertainty at time t, weighted for aggregation; o , is the total k-th category level AVA associated to all relevant sources of valuation uncertainty 1 , … , and valuation positions 1 , … , . Also this AVA is already weighted for aggregation by construction of .
  96. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 96 4: AVA calculation Definitions and basic assumptions [13] Additional Valuation Adjustment (AVA) (cont’d) Notice that:  always include the aggregation weight at any level (valuation exposure, total AVA, total PVA);  ≥ 0 ∀ at any level (valuation exposure, total AVA, total PVA), both pre and post aggregation;  = 0 when the fair value is already prudent w.r.t. the source of valuation uncertainty, = ;  the previous expressions holds both for assets (i > 0) and liabilities (i < 0).
  97. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 97 4: AVA calculation Definitions and basic assumptions [14] Additional Valuation Adjustment (AVA) (cont’d) AVA for derivatives  Remind that for derivatives the total value may be split across different components = 0 + = + + + + ⋯  We assume that such components are not strongly correlated. In particular, we assume that the market value is not strongly correlated with credit and funding risk.  In this case, also the AVAs results to be split across the same components , , , = 0 , , , + , , , + , , , + ⋯
  98. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 98 4: AVA calculation Definitions and basic assumptions [15] Prudent Valuation Adjustment (PVA) The total Prudent Valuation Adjustment (PVA), to be deduced from the CET1, is computed as follows. ≔ () Simplified approach, ෍ =1 Core approach. The detailed AVA aggregation rules under the core approach are discussed within the detailed AVA calculation rules in the following.
  99. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 99 4: AVA calculation Definitions and basic assumptions [16] AVA aggregation The total AVA under the core approach is computed using the following algorithm.  CoPo, FAC, EaT, OpR AVAs are aggregated each as the sum of its corresponding individual components at valuation positions level, each weighted at 100%.  UCS and IFC AVAs are decomposed each into 3 components related to MPU, CoCo and MoRi uncertainties, which are taken into account in the total MPU, CoCo and MoRi AVA aggregation discussed below.  MPU, CoCo and MoRi AVAS are aggregated each as the sum of: o its individual components at valuation positions level o the corresponding UCS and IFC AVA contributions above, o all weighted at 50%.  The total AVA is computed as the simple sum of the residual MPU, CoCo, MoRi, CoPo FAC, EaT, OpR AVAs determined above. In conclusion, the final aggregation includes 50% of MPU, MoRi, CoCo, UCS and IFC AVAs (5 out of 9), and 100% of CoPo FAC, EaT, OpR AVAs (4 out of 9).
  100. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 100 4: AVA calculation Definitions and basic assumptions [17] Definitions summary Item Definition Comments Fair value = ෍ =1 i = index for valuation positions Prudent Value ≤ ∀ = 1, … , , = 1, … , , ∀ = 1, … , o j = index for risk factors o k = index for AVAs Additional Valuation Adjustment (simplified) = 0.1% ෍ =1 + ෍ =1 is the total valuation adjustment at time t Additional Valuation Adjustment (core) ∶= − , : = ෍ =1 ෍ =1 o is the k-th AVA associated to source of valuation uncertainty j and valuation position i at time t, o is the total k-th AVA at t Prudent Valuation Adjustment ≔ () Simplified ෍ =1 Core is the total valuation adjustment at time t
  101. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 101 Price distribution, fair value, fair value adjustment, prudent value, AVA What about real price distributions...? Fair value (mean) Fair value adjusted Prudent value (quantile) Fair value adjustment AVA 4: AVA calculation Definitions and basic assumptions [18]
  102. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 102 4: AVA calculation Data sources Market based Data sourcing (EBA RTS Art. 3) Expert based Consensus service data Proxy data based on similar instruments Application of prudent shifts to valuation inputs Exchange prices in a liquid market Trades in the exact same or very similar instrument, either from internal records or from the market Tradable quotes from brokers and other market participants Identification of natural bounds to the value of an instrument Indicative broker quotes Counterparty collateral valuations
  103. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 103 4: AVA calculation AVA discussion scheme Since AVAs are rather involved and diversified, we need to discuss each AVA using a fixed scheme, including:  AVA definition and regulatory references  AVA scope of application  Fair Value related to the AVA  AVA calculation scheme  Examples  Applications
  104. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 104 4: AVA calculation AVA Market Price Uncertainty (MPU) [1]  AVA definition AVA Market Price Uncertainty (MPU) refers to the valuation uncertainty of a valuation exposure arising from uncertainty of a valuation input. This kind of uncertainty is rather common in price evaluation and may appear in different situations, for example: o when the financial instrument is marked to market (e.g. a bond listed), and there are multiple reliable price contributors; o when the financial instrument is marked to model using some valuation input (e.g. an OTC IRS valued using multiple yield curves based on IRS market quotes), and there are multiple price contributors for the valuation inputs (e.g. multiple IRS market makers).  AVA main references o EBA RTS, article 9. o EBA FAQs 6.1, 21, 23, 23.1, 28, 30, 31, 40.1, 40.3.
  105. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 105 4: AVA calculation AVA Market Price Uncertainty (MPU) [2]  AVA scope of application Within the general prudent valuation scope (see before), AVA MPU regards in particular those valuation positions without either a firm tradable price, or a price that can be determined from reliable data based on a liquid two-way market, and such that at least one valuation input has material valuation uncertainty. AVA MPU shall be computed for all valuation positions , = 1, … , showing a valuation exposure to a valuation input , = 1, … , (valuation exposure level). We stress that a single valuation position may show a valuation exposure to either none, or one, or a few, or many, or all valuation inputs . Thus we may have A , , 1 = 0 and , , 2 ≠ 0 for the same valuation position and two different valuation inputs 1 ≠ 2 .  AVA Fair Value The FV of the trades subject to AVA MPU may include or not the effect of possible MPU. In some particular cases, Institutions may account FV adjustments in their balance sheets to cover possible losses related to MPU. In this case the FV subject to prudent valuation for AVA MPU must include these FV adjustments, or, in other words, such FV adjustments must be subtracted from the AVA MPU (keeping the AVA non-negative).
  106. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 106 4: AVA calculation AVA Market Price Uncertainty (MPU) [3] Does the valuation position have a valuation exposure , = 1, … , , to uncertainty of valuation inputs , = 1, … , ? o Is there firm evidence of a tradable price for the valuation exposure ? o Or can the price for the valuation exposure be determined from reliable data based on a liquid two-way market (as defined in art. 338 of CRR) ? , , = 0 YES Compute individual , , for each valuation exposure to each valuation input Do sources of market data indicate no material valuation uncertainty ? YES YES NO NO AVA Market Price Uncertainty (MPU) (EBA RTS, article 9) refers to the valuation uncertainty of a valuation exposure arising from uncertainty of a valuation input. NO Continue
  107. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 107 4: AVA calculation AVA Market Price Uncertainty (MPU) [4] o Use the data sources defined in Art. 3. o Calculate AVAs on valuation exposures related to each valuation input used in the relevant valuation model. o For non-derivative valuation positions, or derivative positions which are marked to market, refer to the instrument price, or decompose into each valuation input required to calculate the exit price, treated separately. o If a valuation input consists of a (D-dimensional) matrix of parameters, … , calculate , , based on the valuation exposures related to each matrix element … . o If a valuation input does not refer to tradable instruments, map the valuation input and the related valuation exposure to a set of market tradable instruments. Do you reduce the number of parameters of the valuation input (D-dim. matrix) for the purpose of calculating AVAs ? Continue NO P&L variance test Positive YES Negative Subject to independent control function review and internal validation on at least an annual basis
  108. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 108 4: AVA calculation AVA Market Price Uncertainty (MPU) [5] Estimate a point ො within the range with 90% confidence to exit the valuation exposure at that price or better. Use expert-based approach using qualitative and quantitative information available to achieve a prudent value ො with confidence level equivalent to 90%. Do sufficient data exists to construct a range of plausible values for a valuation input ? YES NO Notify competent authorities of the valuation exposures for which this approach is applied, and the methodology used to determine the AVA. Estimate a point ො within the range with 90% confidence that the mid value that could be achieved in exiting the valuation exposure would be at that price or better. Continue Is the range of plausible values of is based on exit prices ? Is the range of plausible values of is based on mid prices ? NO YES
  109. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 109 4: AVA calculation AVA Market Price Uncertainty (MPU) [6] Compute individual AVA MPU , , = , , − , , Apply the valuation input uncertainties ො to valuation exposures and compute prudent value MPUs By revaluation: , , = , , ො or (when the uncertain input is the instrument price): , , = ො By exposure , , = , , − ො − Compute total category level AVA MPU = ෍ =1 ෍ =1 , ,
  110. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 110 4: AVA calculation AVA Market Price Uncertainty (MPU) [7]  AVA calculation o Securities • Impaired/defaulted securities = 0 if the FV is already conservative and does not depend on uncertain market data, otherwise go to next cases. • Liquid securities accounted at Fair Value Level 1 = 0, if the FV is calculated on market tradable prices with negligible bid-ask, otherwise go to next cases. • Contributed securities accounted at Fair Value Level 1 a possible approach is A = ൝ +0.9 × − long positions, −0.9 × − short positions. where / are the lowest/highest bid/ask prices quoted at time t, and = 0.5. • Securities accounted at Fair Value Level 2 or 3 AVA MPU shall be computed via sensitivity or full revaluation based on relevant risk factors, in particular credit spread and interest rate curves, using prudent MPUs.
  111. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 111 4: AVA calculation AVA Market Price Uncertainty (MPU) [8]  AVA calculation (cont’d) o Derivatives AVA MPU is computed via sensitivity or full revaluation based on relevant risk factors.  MPU estimation AVA MPU calculation is based on the estimation of MPUs of relevant (possibly all) risk factors, including volatilities and correlations. Possible sources of MPUs are the following. o Front office traders active in their respective markets. o Appropriate selection of multiple contributors (brokers, market makers) available from data providers (i.e. Bloomberg or Reuters). o Consensus price services (e.g. Markit). o Collateral counterparty valuations for derivatives. o Historical series of prices and market data
  112. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 112 4: AVA calculation AVA Market Price Uncertainty (MPU) [9]  Examples o Bond for which there exist multiple price contributors. o IRS valued using multiple yield curves based on market quotations (Fras, Futures, OIS, IRS, Basis IRS, etc.) for which there exist multiple market makers.
  113. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 113 4: AVA calculation AVA Market Price Uncertainty (MPU) [10] Case study of AVA MPU calculation for a security. • Top left: market bid and ask prices. FV is computed as average mid price = 162.25. • Bottom left: ranking and percentiles of mid prices, AVA MPU for long and short positions, equal to 0.14 and 0.12, respectively. • Top right: distribution chart.
  114. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 114 4: AVA calculation AVA Market Price Uncertainty (MPU) [11] Examples with sensitivities. See EBA RTS sec. 4.1.1 and ref. [23].
  115. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 115 4: AVA calculation AVA Market Price Uncertainty (MPU) [12] P&L variance test Notation  , = 1, … , , = 0, … , = i-th risk factor (scalar, vector or matrix element, generically indexed by i with some ordering) for j-th date (backward time ordered, j = 0 = today, j = 1 = yesterday business day, etc….).  Δ ≔ − −1 = j-th daily variation of risk factor .  = fair value of today’s valuation exposure at j-th date (static portfolio).  ≔ Τ = first-order sensitivity of today’s valuation exposure to risk factor (delta, vega, rho, etc.). Discussion We know the valuation exposure and its fair value at today’s date, 0. Instead, it’s much more difficult to recompute the past fair values of the present valuation exposure, 1 , … , . Thus, we approximate such values using first order Taylor expansion and today’s risk factors sensitivities as follows ≅ −1 + ෍ =1 Δ + ⋯ ≅ −1 + ෍ =1 ,0 Δ .
  116. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 116 4: AVA calculation AVA Market Price Uncertainty (MPU) [13] P&L variance test (cont’d) Notice that we’re assuming that first order sensitivities are fairly constant w.r.t. the risk factors levels, , ≅ ,0 ∀ . This is consistent with first order expansion and the static portfolio assumption. Second order sensitivities (gamma in particular) can be introduced in the Taylor expansion if required. Hence we may define the j-th daily profit & loss of the valuation exposure as : = − −1 ≅ ෍ =1 ,0 Δ , = 1, … , , and we may compute the variance of the historical series as = 1 , … , , Where the EBA RTS requires = 100.
  117. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 117 4: AVA calculation AVA Market Price Uncertainty (MPU) [14] P&L variance test (cont’d) The calculations above may refer to both unreduced and reduced sets of risk factors as well. Denoting reduced quantities with a hat, the reduced set is characterized by a lower number of risk factors, ෡ < . We may calculate the profit & loss of the reduced valuation exposure as ෢ : = ෠ − ෠ −1 ≅ ෍ =1 ෡ መ ,0 Δ , = 1, … , , with the constrain on the total reduced and unreduced sensitivities, ෍ =1 ෡ መ ,0 = ෍ =1 ,0 , for each single risk factor class (e.g. delta, vega, etc.).
  118. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 118 4: AVA calculation AVA Market Price Uncertainty (MPU) [15] P&L variance test (cont’d) Finally, the P&L variance ratio test required by EBA RTS [1], art. 9 can be calculated as = − ෢ ≤ 0.1, where − ෢ = 1 − ෢ 1 , … , − ෢ . Comments The approach above is based on common approximations and requires, beyond the present value and sensitivities of the valuation exposures, just the historical series of the relevant market risk factors. The most important factor driving the result of the test is obviously the choice of the reduced valuation exposure and it’s robustness over time.
  119. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 119 4: AVA calculation AVA Market Price Uncertainty (MPU) [16] P&L variance test (cont’d) Possible issues  How to define the unreduced set of risk factors ? -> choose the tradable nodes.  How to choose the reduced set of risk factors ? This is arbitrary: in principle, institutions are allowed, for each prudent valuation reporting date, to look for the most convenient level of aggregation that minimizes the AVA and passes the test.  How to ensure test stability from time to time ? The test success/failure strongly depends on the distribution of the sensitivity w.r.t. the chosen level of aggregation. Thus the same test applied to a dynamical portfolio may be positive one day and negative another day. Facts Recent experience shows that:  at least for some important cases (i.e. EUR interest rate yield curves and volatilities), extreme aggregations onto a few (1-3) risk factors (pillar, pillar/strike) is often sufficient to pass the test.  Principal component analysis is helpful to understand the most important risk factors and to select the possible aggregations to be tested.  As a consequence, it seems that AVA MPU can be drastically reduced. NEW
  120. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 120 4: AVA calculation AVA Close-Out Costs (CoCo) [1]  AVA definition AVA Close-Out Costs (CoCo) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in the exit price of the valuation positions, or, in other terms, the cost of liquidity that a particular valuation exposure can exhibit in particular market conditions. Both situations lead to relevant bid-ask spreads to exit the valuation position. Since illiquidity can also be seen as uncertainty around the mid price, AVA CoCo overlaps with AVA MPU. Thus, when AVA MPU is based on tradable prices, AVA CoCo may be set to zero.  AVA main references o EBA RTS, article 10. o EBA FAQs 23, 24, 24.1, 28, 30, 31, 37, 37.1, 40.1, 40.3, 42.5.  AVA scope of application Within the general prudent valuation scope (see before), AVA CoCo refers in particular to those valuation positions for which there is not sufficient liquidity to exit the valuation exposure at mid price (at 90% confidence level), and there are relevant bid-ask spread.
  121. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 121 4: AVA calculation AVA Close-Out Costs (CoCo) [2]  AVA Fair Value The FV of the trades subject to AVA CoCo may include or not the effect of possible bid-ask spread. In some particular cases, Institutions may account FV adjustments in their balance sheets to cover the most relevant bid-ask uncertainties. In this case the FV subject to prudent valuation for AVA CoCo must include such FV adjustments, or, in other words, such FV adjustments must be subtracted from the AVA CoCo (keeping the AVA non-negative).
  122. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 122 4: AVA calculation AVA Close-Out Costs (CoCo) [3] Did you calculate for the same valuation exposure based on exit prices ? o Did you compute the mark to market on the assumption to close out at mid market (see CRR art. 105.5) ? o Is there evidence that sufficient liquidity exists to exit the valuation exposure at mid-price at 90% confidence level ? NO Compute individual for each valuation exposure to each bid-offer spread Δ for each valuation input YES YES AVA Close Out Cost (CoCo) (EBA RTS, article 10) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in the exit price of the valuation positions. NO Continue , = 0 Does the valuation position have a valuation exposure , = 1, … , , to uncertainty of exit price ? NO YES
  123. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 123 4: AVA calculation AVA Close-Out Costs (CoCo) [4] o Use the data sources defined in Art. 3. o For non-derivative valuation positions, or derivative positions which are marked to market, either refer to the instrument price, or decompose into each valuation input required to calculate the exit price, treated separately. o If a valuation input consists of a matrix of parameters, calculate AVA based on the valuation exposures related to each matrix element. o If a valuation input does not refer to tradable instruments, map the valuation input and the related valuation exposure to a set of market tradable instruments. Reduce the number of parameters of the valuation input for the purpose of calculating AVAs ? Continue NO P&L variance test Positive YES Negative Subject to independent control function review and internal validation on at least an annual basis
  124. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 124 4: AVA calculation AVA Close-Out Costs (CoCo) [5] Estimate a point ෡ Δ within the range with 90% confidence that the bid-ask spread that could be achieved in exiting the valuation exposure would be at that price or better. Use expert-based approach using qualitative and quantitative information available to achieve a level of certainty in the prudent value෡ Δ that is equivalent to 90%. Do sufficient data exists to construct a range of plausible bid- offer spreads Δ for a valuation input ? YES NO Notify competent authorities of the valuation exposures for which this approach is applied, and the methodology used to determine the AVA. Continue
  125. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 125 4: AVA calculation AVA Close-Out Costs (CoCo) [6] Compute individual APVA CoCo , , = , , − , , Apply half of the bid-offer spread ෡ Δ to valuation exposure and compute prudent value Compute total category level AVA CoCo = ෍ =1 ෍ =1 , , By exposure: , , = , , − 1 2 ෡ Δ By revaluation: , , = , , ± 1 2 ෡ Δ , or (when the uncertain input is the instrument price): , , = , , − 0.5 × ෡ Δ
  126. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 126  AVA calculation o Securities • Securities held in market making portfolios = 0, since, in these cases, the Institution makes both the bid and the ask prices. • Liquid securities accounted at Fair Value Level 1 a possible approach is A = () ൝ −ത long positions, +ത short positions. where ത ()/ത are the average bid/ask prices quoted at time t, and = 0.5. • Any other security  = 0 if, according to the Institution Fair Value Policy, they are already priced at prudent bid or ask,  otherwise AVA CoCo shall be computed via sensitivity or full revaluation based on relevant risk factors, in particular credit spread and interest rate curves, using prudent bid-ask spread. 4: AVA calculation AVA Close-Out Costs (CoCo) [7]
  127. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 127  AVA calculation (cont’d) o Derivatives AVA CoCo is computed via sensitivity or full revaluation based on relevant risk factors and on market price uncertainty in the bid-offer spread.  Exchange Traded Derivatives (ETD) A = 0, since the FV is quoted and actively traded on the exchange with negligible bid-ask, otherwise go to next case.  OTC Derivatives (OTCD) AVA CoCo may be computed typically via full revaluation or sensitivity based on relevant risk factors, similarly to AVA MPU.  Bid-ask MPU estimation AVA CoCo calculation is based on the estimation of bid-ask MPUs of relevant risk factors. Possible sources of such MPUs are restricted to those cases where the market quotes multiple sources of bid-ask spread.  Examples o Bond for which there exist multiple bid-ask contributors. 4: AVA calculation AVA Close-Out Costs (CoCo) [8]
  128. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 128 Case study of AVA CoCo calculation for a security.  Top left: long positions, ranking and percentiles of mid-bid differences, AVA CoCo = 0.71.  Top right: short positions, ranking and percentiles of ask-mid differences, AVA CoCo = 0.71. 4: AVA calculation AVA Close-Out Costs (CoCo) [9]
  129. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 129  AVA definition AVA Model Risk (MoRi) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in models and model calibrations used by market participants. In particular, AVA MoRi does not refers to the uncertainty in market risk capital arising from model risk (see FAQ 23.1).  AVA main references o EBA RTS, article 11. o EBA FAQs 10, 23.1, 28.  AVA scope of application Within the general prudent valuation scope (see before), AVA MoRi refers in particular to those valuation positions for which the Institution estimates that there is a lack of firm exit price due to model and/or model calibration choices. Of course, instruments which can be replicated by exact static combination of mark-to-market instruments should not contribute to AVA MoRi. 4: AVA calculation AVA Model Risk (MoRi) [1]
  130. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 130  AVA Fair Value The FV of the trades subject to AVA MoRi may include or not the effect of possible model risk. In some particular cases, Institutions may account FV reserves in their balance sheets to cover the most relevant model risk uncertainties. In this case the FV subject to prudent valuation for AVA CoCo must include these reserves, or, in other words, the reserves must be subtracted from the AVA MoRi (keeping the AVA non-negative). 4: AVA calculation AVA Model Risk (MoRi) [2]
  131. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 131 Does the valuation position , = 1, … , , valued with model , = 1, … , , lacks of a firm exit price ? YES AVA Model Risk (MoRi) (EBA RTS, article 11) refers to the valuation uncertainty of a valuation exposure arising from uncertainty in model usage and calibrations used by market participants. Continue 4: AVA calculation AVA Model Risk (MoRi) [3] NO Is the valuation position , valued with model , sensitive to the usage of different valuation models or model calibrations 1 , … , used by market participants ? , , = 0 YES Compute individual , , for each applicable valuation model 1 , … , Does the valuation model risk arise from calibrations from market derived parameters ? NO NO YES To be included into Notation: the model scenarios 1 , … , includes all the possible models and calibrations appropriate to revaluate all the valuation positions Notation: typically, for a given valuation exposure , a single valuation model is used
  132. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 132 4: AVA calculation AVA Model Risk (MoRi) [4] Estimate a point ෢ , , within the range with 90% confidence to exit the valuation exposure at that price or better. Use expert-based approach to estimate a prudent value ෢ , , considering: o complexity of products relevant to the model; o diversity of possible mathematical approaches and model parameters, not related to market variables; o one way market for relevant products; o existence of unhedgeable risks in relevant products; o model adequacy to capture the behavior of the pay-off of the products in the portfolio. Is it possible to construct a range of plausible valuations produced from model scenarios 1 , … , ? YES NO Notify competent authorities of the models for which this approach is applied, and the methodology used to determine the AVA. Model risk test Continue
  133. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 133 4: AVA calculation AVA Model Risk (MoRi) [5] Compute individual APVA MoRi , , = , , − , , Compute total category level AVA MoRi = ෍ =1 ෍ =1 , , Compute individual prudent value MoRi , , = ෢ , , Notation: ෢ , , denotes the prudent value of the valuation exposure evaluated with model determined as above
  134. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 134 4: AVA calculation AVA Model Risk (MoRi) [6] Find a material sample of valuation models ෩ ⊂ 1 , … , for which AVA MoRi is computable via range of plausible values (art. 11.3) Model risk test For each valuation position subject to AVA MoRi computed via expert-based approach (EBA RTS art. 11.4) Compute AVA MoRi using expert based approach (art. 11.4) applied to the sample of models ෩ Compute AVA MoRi using a range of plausible values (art. 11.3) applied to the sample of models ෩ Compare the results and check the prudence of the expert-based approach with annual frequency
  135. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 135  AVA calculation o Securities • Securitizations AVA MoRi may be calculated by stressing cash flows w.r.t. constant default rate (CDR) and constant prepayment rate (CPR). • CDOs AVA MoRi my be calculated by stressing correlations, recoveries and weighted average life (WAL). • Impaired/defaulted securities AVA MoRi is calculated by stressing the recovery rate. o Derivatives AVA MoRi may be computed using alternative models and/or model calibrations applied to the corresponding valuation exposures. 4: AVA calculation AVA Model Risk (MoRi) [7]
  136. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 136  Alternative models and calibrations AVA MoRi is not based on any possible alternative model or model calibration, but on those specific alternative models or model calibrations that may reasonably used by market participants to price the same or similar valuation exposures.  Examples o alternative but reasonable models, • calibrated to the same calibration basket • Referred to the same group of financial instruments o Same model, alternative calibration approaches, e.g. • different calibration baskets • different calibration weights (e.g. flat, or vega weighted) • different objective functions • different optimization algorithm (e.g. global vs local) • Etc. o Same model, same calibration, alternative numerical approaches, e.g. • analitycal approximations • semi-analitycal approximations • numerical PDE solution • Monte Carlo simulation • etc. 4: AVA calculation AVA Model Risk (MoRi) [8] Inspiration: «There’s plenty of room at the bottom» Richard Feynman, 1959 www.its.caltech.edu/~feynm an/plenty.html
  137. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 137  Market Risk Scenarios vs Model Risk Scenarios o Risk measures are typically linked to scenarios o Scenarios are related to the risk factors relevant for a particular risk typology 4: AVA calculation AVA Model Risk (MoRi) [9] Risk class Scenarios Risk measures Market risk Present market data VaR, Expected shortfall, etc. Counterparty risk Future market data EPE, Effective EPE, etc. Operational risk Operational loss event frequency and severity VaR 99.9% Model risk Model scenarios o Alternative models o Alternative numerical approaches o Alternative calibrations K-th percentile of distribution of model prices (10° percentile for Prudent Valuation)
  138. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 138  Processes and controls relevant to model risk (EBA RTS art. 19.2, 19.3) o Annual review of model performance o Independence in the validation process between risk taking and control units, o Institution-wide product inventory ensuring that every valuation position is uniquely mapped to a product definition o Defined valuation methodologies for each product of the inventory, including calibration and measurement of the valuation uncertainty. o Validation process ensuring that for each product, the product level methodologies are approved o Defined thresholds based on observed market data for determining when valuation models are no longer sufficiently robust o A new product approval process referencing the product inventory 4: AVA calculation AVA Model Risk (MoRi) [10]
  139. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 139 4: AVA calculation AVA Model Risk (MoRi) [11] Relationships between AVA MoRi and AVA MPU, AVA CoCo, fair value, fair value adj. AVA = 0.5xMPU + 0.5xCoCo + 0.5xMoRi Fair value (mean) Fair value adjusted MPU adj. Fair value adj.MoRi AVA MoRi CoCo adj. AVA CoCo AVA MPU MoRi adj.
  140. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 140 4: AVA calculation AVA Model Risk (MoRi) [12] Historical sources of model risk Period Main driver Main risk factor Effects 1987 Black Monday Volatility Volatility smile 2004 CMS market Volatility Swaption volatility smile and CMS convexity adjustment 2004 IAS39 Credit Credit Risk Adjustment (CRA) 2007 Credit crunch Credit, liquidity Subprime writedown 2007 Credit crunch Interest rate basis Multiple yield curves 2009-2010 Credit crunch Interest rate basis CSA discounting 2009-2010 Credit crunch Bilateral credit CVA & DVA (IFRS13, 2013) 2013-2015 Credit crunch Funding Funding Valuation Adjustment (FVA) 2013-2014 Credit crunch Interest rate Negative interest rates and inflation, negative Floor strikes, Bond floater coupons floored, end of Black’s model. 2014- Credit crunch Capital charges Capital Valuation Adjustment (KVA) 2017 Credit crunch Funding Bilateral initial margins
  141. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 141  Market Risk Scenarios vs Model Risk Scenarios o Risk measures are typically linked to scenarios o Scenarios are related to the risk factors relevant for a particular risk typology 3: AVA calculation AVA MoRi: model risk scenarios vs traditional scenarios Risk class Scenarios Risk measures Market risk Present market data VaR, Expected shortfall, etc. Counterparty risk Future market data EPE, Effective EPE, etc. Operational risk Operational loss event frequency and severity VaR 99.9% Model risk Model scenarios o Alternative models o Alternative numerical approaches o Alternative calibrations K-th percentile of distribution of model prices (10° percentile for Prudent Valuation)
  142. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 142 3: AVA calculation AVA MoRi: model risk scenarios for interest rate derivatives
  143. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 143 3: AVA calculation AVA MoRi: model risk scenarios nested simulation Pricing model One Pricing model Two Pricing model Three  Idea of model risk in nested Monte Carlo Simulations for XVAs o Scenarios are related to the risk factors relevant for a particular risk typology o Primary scenarios are tranched into different groups, associated to different simulation dynamics o At each future time simulation date, we use different pricing models, each consistent with its underlying risk factors dinamics. NEW
  144. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 144 4: AVA calculation AVA Model Risk (MoRi): case study 1 [1] Case study 1: model risk in interest rate yield curve construction  Interest rate yield curves are used everywhere for discounting and for interest rate derivatives and securities with floating rate coupons. So, this is an important case study.  Yield curve construction is based on recursive application of pricing formulas applied to interest rate market instruments. So, there is a lot of modelling inside.  In particular, the interpolation algorithm is very important, both pre and post bootstrapping: o Simple but non-smooth linear interpolation algorithms are very simple and robust, but produces irregular forward curves o Standard spline interpolation is less simple but produces oscillating yield curves o Monotonic cubic spline interpolation is regular.
  145. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 145 4: AVA calculation AVA Model Risk (MoRi): case study 1 [2] Linear interpolation on zero interest rates Monotonic cubic spline interpolation on zero interest rates
  146. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 146 4: AVA calculation AVA Model Risk (MoRi): case study 1 [3]  Differences in bps between three different interpolation algorithms (linear, natural cubic spline and monotonic cubic spline) for a portfolio of 3 standard IRS on Euribor 1M, 6M, 12M + 3 standard Basis Swaps.
  147. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 147 4: AVA calculation AVA Model Risk (MoRi): case study 2 [1] Case study 2: model risk experiment with Numerix  Sensitivity of prices to models o Various dimensions of modelling decisions o Example of Bermudan swaption pricing with HW1F, HW2F, CIR, and BK models o Impact of calibration choices o AVA MoRi for a Bermudan swaption o Model implied European swaption smile  Impact of changing market environment on model performance o Handling of negative rates o Example of floor pricing with very low strikes by using various models  Joint work with Ilja Faerman and Laure Darleguy, Numerix webinar, 12 Nov. 2014, available at www.numerix.com
  148. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 148 4: AVA calculation AVA Model Risk (MoRi): case study 2 [2] Case study 2: model risk experiment with Numerix (cont’d)  Global modelling approach Trade FX spot Basis spread Yield Curve Correlation Model underlying Forward curve Swap rate Risk factor Short-rate Distribution type Normal Log-normal Mixture Chi- squared Model type HW1F HW2F Calibration instruments Caplets Swaptions Instruments configuration 10Y diagonal 20Y diagonal 10Y column 10Y diag + 10Y column CIR BK CMS … … … … … …
  149. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 149 4: AVA calculation AVA Model Risk (MoRi): case study 2 [3] Case study 2: model risk experiment with Numerix (cont’d) Experiment # Instruments Models Calibrations Bermudan swaption • Coterminal bermudan payer swaption • Euribor 6M • 10Y maturity • Annual callability • Sstrike ATM 10Y swap • OIS discounting • Hull-White 1 Factor (HW1F) • Black-Karasinski (BK) • Cox-Ingersoll-Ross 1 Factor (CIR1F) • Hull-White 2 Factors (HW2F) • Cox-Ingersoll-Ross 2 Factors (CIR2F) • Set 1: 10 Y diagonal swaption ATM • Set 2: 10Y diagonal and 1Y column swaption ATM • Set 3: 20Y diagonal and 1Y column swaption ATM Caps/Floors with negative rates • 5Y Floor • Euribor 6M • Negative and positive strikes • Yield curves with negative rates • Linear interpolation and flat extrapolation • SABR interpolation and flat extrapolation • Black (analytic) • Hull-White 1 Factor (HW1F) • Shifted Black-Karasinski (SBK) • Set 1: Cap volatility columns for strikes ATM and 1% • Set 2: full Cap volatility surface, with strikes from 1% to 10% Joint work with Ilja Faerman and Laure Darleguy, Numerix webinar, 12 Nov. 2014, www.numerix.com
  150. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 150 4: AVA calculation AVA Model Risk (MoRi): case study 2 [4] Overview of results  Prices range from 1.45% to 3.91%  Normal models produce consistently higher PVs for all calibration sets compared to non-normal models HW1F BK CIR1F HW2F CIR2F 0.00% 1.00% 2.00% 3.00% 4.00% Set1 Set2 Set3 Bermudan swaption prices per model and calibration set
  151. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 151 4: AVA calculation AVA Model Risk (MoRi): case study 2 [5] Results by calibration set  Calibration set 1 (10Y diagonal) produces highest distribution of prices  Average price is fairly stable across different calibration sets  Same model stays consistently below or above the average price for all calibration sets 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% Set1 Set2 Set3 Bermudan swaption prices per calibration set HW1F BK CIR1F HW2F CIR2F Average
  152. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 152 4: AVA calculation AVA Model Risk (MoRi): case study 2 [6] Results by model  HW1F and BK models exhibit lowest variations in prices with changing calibration set  Prices of 1F and 2F models of the same model type can differ significantly 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% HW1F BK CIR1F HW2F CIR2F Bermudan swaption prices per model Set1 Set2 Set3
  153. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 153 4: AVA calculation AVA Model Risk (MoRi): case study 2 [7] Results  Notional is 10m EUR  Assuming Fair Value is the average of all price  Long swaption: o Fair Value: FV = 258k EUR o Prudent value is the 10% percentile of all prices: PV = 177k EUR o AVA MoRi = 0.5x(FV-PV) = 40.5k EUR  Short swaption: o Fair Value: FV = -258k EUR o Prudent value is the 90% percentile of all prices: PV = -317k EUR o AVA MoRi = 0.5x(FV-PV) = 29.5k EUR
  154. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 154 4: AVA calculation AVA Model Risk (MoRi): case study 2 [8] Excluding models All models All except HW2F All models All except HW2F Fair Value (1) 258 258 -258 -258 Prudent Value 177 158 -317 -315 Model Risk AVA 40.5 50 29.5 28.5 Long swaption Short swaption Fair Value (1) is computed as the average of all model prices Fair Value (2) for “All except HW2F” is computed excluding the price of the HW2F model All models All except HW2F All models All except HW2F Fair Value (2) 258 240 -258 -240 Prudent Value 177 158 -317 -315 Model Risk AVA 40.5 41 29.5 37.5 Short swaption Long swaption
  155. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 155 4: AVA calculation AVA Model Risk (MoRi): case study 2 [9] Exercise probabilities 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23 Call probabilities per coupon Calibration set 1 HW1F BK CIR HW2F CIR2F 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23 Call probabilities per coupon Calibration set 2 HW1F BK CIR HW2F CIR2F 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% Oct-15 Oct-16 Oct-17 Oct-18 Oct-19 Oct-20 Oct-21 Oct-22 Oct-23 Call probabilities per coupon Calibration set 3 HW1F BK CIR HW2F CIR2F Exercise probability per coupon  CIR-type models imply a higher probability of early exercise than HW models  The term structure of exercise probabilities is regular for all models for calibration set 1, humped for calibration sets 2 and 3.
  156. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 156  AVA definition AVA Unearned Credit Spread (UCS) refers to the valuation uncertainty in the credit valuation adjustment (CVA) to include, according to the applicable accounting framework, the current value of expected losses due to counterparty default on derivative positions. Such valuation uncertainty refers, in particular, to MPU, CoCo and MoRi uncertainties in the calculation of CVA. Hence, the RTS specifies that the AVA UCS shall be split into such components, to be aggregated to their corresponding AVA. Since the definition of AVA UCS specifies “losses due to counterparty default” (not “profits due to own default”), and the CRR, art. 33 states that the debt valuation adjustment (DVA, the gain on liabilities due to own credit quality) should not be included in the calculation of own funds, then AVA UCS shall not include the DVA component.  AVA main references o EBA RTS, article 12. o EBA FAQs 10, 25, 28. 4: AVA calculation AVA Unearned Credit Spread (UCS) [1]
  157. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 157  AVA scope of application Within the general prudent valuation scope (see before), AVA UCS refers in particular to those valuation positions subject to a credit valuation adjustment, and specifically, to OTC derivatives, with a particular focus on uncollateralized derivatives. Securities are excluded, since credit risk is already included in the security credit spread.  AVA Fair Value The FV of the trades subject to AVA UCS may include full, partial or null CVA. In any case the FV subject to prudent valuation for AVA UCS must include these CVAs. 4: AVA calculation AVA Unearned Credit Spread (UCS) [2]
  158. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 158 4: AVA calculation AVA Unearned Credit Spread (UCS) [3] AVA Unearned Credit Spread (UCS) (EBA RTS, article 12) refers to the valuation uncertainty in the credit valuation adjustment to include, according to the applicable accounting framework, the current value of expected losses due to counterparty default on derivative positions. o Is the valuation position , = 1, … , , a derivative position, and o according to the applicable accounting framework, is an adjustment necessary to include the current value of expected losses due to counterparty default (CVA) ? YES NO , = 0 Aggregate , , to APVA MPU. Go to AVA MPU and apply those rules to compute individual AVA UCS w.r.t. MPU, , , Aggregate , , to APVA CoCo. Go to AVA CoCo and apply those rules to compute individual AVA UCS w.r.t. CoCo, , , Aggregate , , to APVA MoRi. Go to AVA MoRi and apply those rules to compute individual AVA UCS w.r.t. MoRi, , ,
  159. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 159  AVA calculation o Securities: excluded o Derivatives • DVA component = 0, since DVA is excluded from the prudent valuation scope. • CVA component shall be calculated considering the following components.  Unilateral CVA: since DVA is excluded, Institutions shall consider the unilateral CVA, without first to default conditioning.  , : uncertainty in CDS spreads, PDs and recovery rates, uncertainty in risk factors used to compute the exposure (e.g. curves, volatilities)  , : bid/ask in CDS spreads.  , : unilateral vs bilateral CVA, time simulation grid, risk free vs risky close-out, wrong way risk, different dynamics to simulate underlying risk factors and compute the exposure. • No CVA case if the CVA is not included in the accounting fair value for some valuation positions, shall be equal to the full CVA of those position, calculated using prudent parameters as above. 4: AVA calculation AVA Unearned Credit Spread (UCS) [4]
  160. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 160  AVA definition AVA Investing and Funding Costs (IFC) refers to the valuation uncertainty in the funding costs used when assessing the exit price of a valuation position, according to the applicable accounting framework. Such valuation uncertainty refers, in particular, to MPU, CoCo and MoRi uncertainties in the calculation of the funding cost. Hence, AVA IFC shall be split into such components, to be aggregated to their corresponding AVAs.  AVA main references o EBA RTS, article 13. o EBA FAQs 26, 35, 36.  AVA scope of application Within the general prudent valuation scope (see before), AVA IFC refers in particular to those valuation positions subject to a funding valuation adjustment and specifically, to OTC derivatives. Securities are excluded, since funding risk is already included in the security credit spread  AVA Fair Value The FV of the trades subject to AVA IFC may include full, partial or null FVA. In any case the FV subject to prudent valuation for AVA IFC must include these FVAs. 4: AVA calculation AVA Investing and Funding Costs (IFC) [1]
  161. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 161 4: AVA calculation AVA Investing and Funding Costs (IFC) [2] AVA Investing and Funding Cost (IFC) (EBA RTS, article 13) refers to the valuation uncertainty in the funding costs used when assessing the exit price according to the applicable accounting framework o Is the valuation position , = 1, … , , a derivative position, and o according to the applicable accounting framework, is an adjustment necessary to include the funding costs in the exit price (FVA) ? YES NO , = 0 Aggregate , , to APVA MPU. Go to AVA MPU and apply those rules to compute individual AVA IFC w.r.t. MPU, , , Aggregate , , to APVA CoCo. Go to AVA CoCo and apply those rules to compute individual AVA IFC w.r.t. CoCo, , , Aggregate , , to APVA MoRi. Go to AVA MoRi and apply those rules to compute individual AVA IFC w.r.t. MoRi, , ,
  162. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 162  AVA calculation o Securities: excluded o Derivatives • Strongly collateralized derivatives = 0 if the funding cost is already included in the FV using OIS discounting methodology. • Non-Strongly collateralized derivatives  If the FVA is included in the accounting FV for some valuation positions, AVA IFC shall be calculated as the FVA uncertainty, resulting from the uncertainty in the funding curve.  If the FVA is not included in the accounting FV for some valuation positions, shall be equal to the full FVA of those position, calculated using prudent parameters. • CSA with initial margins AVA IFC shall computed on the initial margins, using a discounting approach applied to an exposure profile assigned to the future initial margin. 4: AVA calculation AVA Investing and Funding Costs (IFC) [3]
  163. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 163 4: AVA calculation AVA Investing and Funding Costs (IFC) [4] • shall be calculated considering the following components.  , : uncertainty in funding spreads, PDs and recovery rates, uncertainty in risk factors used to compute the exposure (e.g. curves, volatilities)  , : bid/ask in funding spreads.  , : time simulation grid, different dynamics to simulate underlying risk factors and compute the exposure.  Funding spread estimation AVA IFC calculation is based on the estimation of a prudent funding curve. Possible sources of such yield curve is the bond yield curve based on own Institution bond emissions.
  164. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 164 4: AVA calculation AVA Investing and Funding Costs (IFC) [5] Switch to FVA accounting “[JPM] implemented a FVA framework this quarter for its OTC derivatives and structured notes, reflecting an industry migration towards incorporating the cost or benefit of unsecured funding into valuations. For the first time this quarter, we were able to clearly observe the existence of funding costs in market clearing levels. As a result, the firm recorded a $1.5 billion loss this quarter.” (source: M. Cameron, Risk Magazine, 14 Jan. 2014) Bank 2012 2013 Barclays -£101 MM ? Deutsche Bank -- -€364 MM Goldman Sachs ? ? JP Morgan -- -$1.500 MM Lloyds Banking Group - £143 MM -£135 MM Nomura -- -¥10.000 MM (-$98 MM) Royal Bank of Scotland - £475 MM -£424 MM Societè Generale ? ? UBS -- --
  165. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 165  AVA definition AVA Concentrated Positions (CoPo) refers to the valuation uncertainty in the exit price of concentrated positions. Such valuation uncertainty refers, in particular, to those valuation positions showing concentrated exposures related to: o the size relative to the liquidity of the related market; o the average daily market volume and typical daily trading volume of the institution; o the institution’s ability to trade in that market, and to exit the valuation position within the time horizon implied by the market risk capitalization (10 days) without impacting the market.  AVA main references o EBA RTS, article 14. o EBA FAQs 32, 33, 34.  AVA scope of application Within the general prudent valuation scope (see before), AVA CoPo refers in particular to those valuation positions subject to concentration risk as defined above.  AVA Fair Value The FV of the trades subject to AVA CoPo typically does not include a CoPo component. 3: AVA calculation AVA Concentrated Positions (CoPo) [1]
  166. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 166 3: AVA calculation AVA Concentrated Positions (CoPo) [2] AVA Concentrated Positions (CoPo) (EBA RTS, article 14) refers to the valuation uncertainty in the exit price of concentrated positions Identify concentrated valuation positions , = 1, … , , considering: o the size of all valuation positions relative to the liquidity of their related market, o the institution’s ability to trade in that market, o the average daily market volume and typical daily trading volume of the institution. YES NO , = 0 For each concentrated valuation position , there exists a market price applicable for the size of the position ? Estimate a prudent exit period Does the prudent exit period exceed 10 days ? Continue YES NO
  167. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 167 3: AVA calculation AVA Concentrated Positions (CoPo) [3] Compute individual AVA CoPo taking into account: o the volatility of the valuation input, o the volatility of the bid offer spread, o the impact of the hypothetical exit strategy on market prices. Document the methodology applied to determine concentrated valuation positions for which a concentrated positions AVA is calculated Compute total category level AVA CoPo = ෍ =1 ,
  168. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 168  AVA calculation o Securities AVA CoPo may be calculated as follows: • Look for possible concentrated positions by comparing the size held w.r.t. the outstanding amount of the security circulating on the market, • estimate coefficients of uncertainty related to the sizes above, • compute AVA CoPo via sensitivity on the credit risk factors and uncertainties above. o Derivatives OTC derivatives typically do not show concentrated positions in the sense defined above. Possible exceptions shall be documented and AVA CoPo shall be calculated as described in the previous scheme.  Examples o Concentrated positions into single stock w.r.t. typical stock trading volumes o Concentrated positions into single bond emissions w.r.t. typical bond trading volumes and outstanding amount. 3: AVA calculation AVA Concentrated Positions (CoPo) [4] w.r.t. typical stock trading volumes
  169. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 169  AVA definition AVA FAC takes into account the valuation uncertainty emerging from possible administrative costs and future hedging costs on valuation positions for which a direct exit price is not applied for the close-out costs AVA. Thus, future administrative costs are complementary to close-out costs. If the close-out costs are assessed on a full exit price basis then, after executing the corresponding close out strategy, the positions disappear, and there are no future administrative costs. However, where close-out costs are assessed on a "cost-to hedge" basis, as with derivative portfolios, the positions are maintained, and therefore there are possible future administrative costs in running the portfolio until maturity.  AVA main references o EBA RTS, article 15. o EBA FAQs 37, 37.1.  AVA scope of application Within the general prudent valuation scope (see before), AVA CoPo refers in particular to those valuation positions subject to FAC as defined above. 4: AVA calculation AVA Future Administrative Costs (FAC) [1]
  170. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 170  AVA Fair Value The FV of the valuation positions typically does not include the effect of possible future administrative costs, since such costs are specific of each institution and do not regard an exit price according to IFRS. Hence, the AVA FAC must be applied directly to the full FV of valuation positions. 4: AVA calculation AVA Future Administrative Costs (FAC) [2]
  171. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 171 4: AVA calculation AVA Future Administrative Costs (FAC) [3] AVA Future Administrative Costs (FAC) (EBA RTS, article 15) refers to the valuation uncertainty due to future administrative and hedging costs YES , = 0 Do you calculate and for a valuation exposure , = 1, … , ,, which imply fully exiting the exposure ? Compute individual APVA FAC taking into account: o administrative costs, including all incremental staffing and fixed costs that will be incurred in managing the portfolio, over the expected life of the valuation exposures, o the future hedging costs over the expected life of the valuation exposures, o the cost reduction as long as the size of the valuation exposure reduces, o the term structure of discounts at risk free rate. NO Compute total category level AVA FAC = ෍ =1 ,
  172. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 172 4: AVA calculation AVA Future Administrative Costs (FAC) [4]  AVA calculation Considering the regulatory requirements, we may write a general formula for AVA FAC , = න , , , , , where o , = discount factor over the time interval , , o , , = administrative costs expected at time t for future time interval , + , per unit of currency, o , , , = nominal of the valuation exposure at future time u, o T = exipry date of the valuation exposure Considering constant administrative costs and a decreasing step-wise constant notional struck on dates 1 , … , , < 1 , = , we may write a discrete formula , ≅ , ෍ =1 , , , − −1 . Considering furthermore a single (weighted) average lifetime (WAL) we may further simplify to , ≅ , , − .
  173. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 173 4: AVA calculation AVA Future Administrative Costs (FAC) [5]  AVA calculation (cont’d) Clearly, the administrative cost , is the most difficult data to obtain. We stress that in the formula above , refers to the cost per unit of time and currency, not to the total cost of the desk or the institution, which manage other portfolios not subject to AVA.  AVA data AVA FAC calculations require the following input data. o Valuation positions not at full exit price, with nominal amounts and maturities. o Administrative and hedging costs per unit of time, per currency, per desk, per activity. o Risk free (OIS) discount term structure until portfolio maturity.
  174. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 174  AVA definition AVA Early Termination (EaT) refers to the valuation uncertainty emerging from potential losses arising from non-contractual early terminations of client trades.  AVA main references o EBA RTS, article 16. o EBA FAQs 38.  AVA scope of application Within the general prudent valuation scope (see before), AVA EaT regards in particular client trades, that is, trades with client counterparties that may be subject to non-contractual early termination because of litigations or commercial reasons.  AVA Fair Value The FV of the client trades subject to AVA EaT typically does not include the effect of possible non-contractual early terminations by clients. In some particular cases, Institutions may account reserves in their balance sheets to cover possible losses related to early terminations of some trades or portfolios with specific counterparties. If these reserves are accounted as a FV component, the FV subject to prudent valuation for AVA EaT must include the reserves. In other words, the reserves must be subtracted from the AVA EaT. 4: AVA calculation AVA Early Termination (EaT) [1]
  175. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 175 4: AVA calculation AVA Early Termination (EaT) [2] AVA Early Termination (ET) (EBA RTS, article 16) reflects the valuation uncertainty arising from potential losses due to possible non-contractual early terminations of client trades. YES Is the valuation position , = 1, … , , subject to possible non-contractual early termination ? Identify a suitable past time window ; and historical trades = 1, … , subject to non-contractual early terminations at past dates , … , 1 such that ≤ ≤ ⋯ ≤ 1 ≤ . NO Retrieve the corresponding historical fair values , and actual termination prices , . Continue , = 0
  176. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 176 4: AVA calculation AVA Early Termination (EaT) [3] The 10th percentile may be negative (loss) or positive (profit), and represents the highest loss or the smallest profit realized with 90% historical probability. Compute individual APVA EaT according to the formula , = ቊ 0, 10% ≥ 0, 10% × , 10% < 0. Calculate o the historical profit and loss values, , ∶= ൗ , − , , , o the historical P&L distribution, Τ Δ Δ , o the 10th percentile of the P&L distribution, 10% ≔ ℙ Τ Δ Δ , 10% , Compute total category level AVA EaT = ෍ =1 ,
  177. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 177 4: AVA calculation AVA Early Termination (EaT) [4]  AVA calculation See flow chart above.  AVA data AVA EaT calculations require a database of historical early terminations, including, for each trade: o termination date, o nominal, o fair value at EaT time instant, o actual EaT price at EaT time instant.  Examples o Trades early terminated because of litigations o Trades early terminated because of commercial relationships
  178. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 178 4: AVA calculation AVA Early Termination (EaT) [5]  Case study See figure below.
  179. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 179 4: AVA calculation AVA Early Termination (EaT) [6]  Case study (cont’d) o The nominal of the present portfolio of client trades subject to possible non-contractual EaT (cols. 2-4 top, 12 €mln) is taken from “Derivatives HFT” in the sample portfolio. o The absolute FV is set to 5% of the nominal for 1,000 trades. o The past portfolio is set to half the present portfolio and may be seen as an average over the EaT historical window (so, trading volume increased from past to present). o The portfolio of client trades that were historically early terminated (cols. 5-7 top) is set to 1% of the past portfolio, hence the historical probability of non-contractual EaT is 1%. o In the bottom table we show a possible drill-down of the 10 trades historically affected by non-contractual EaT. We generated the absolute EaT price (col. 4) as P=FV(1+10%ε), where ε is a random number with uniform distribution in [-1,1]. o Hence, the P&L (cols. 5-6) may be positive or negative (we chose a negative case). o Given the relative P&L% distribution (col. 6), we calculated the 10th percentile (which, in this simple case with 10 trades, is just the 2nd higher P&L%), representing the highest loss happened with 90% historical probability after non-contractual EaT. o Finally, we applied such historical estimate to the absolute FV of the present portfolio in the top table (col. 9-10). o The AVA (col. 11) is just the absolute value of the corresponding expected loss (col. 9). o We notice that the historical P&L%(10) (-9.64%) corresponds to a small historical loss (- 28,917€) originated by a single deal with limited fair value (300.000€) but generates a much larger expected loss (-578,346€) once applied to the fair value of the present portfolio (6,000,000€). This is consistent with the idea of prudent value at 90% confidence level required by the regulation.
  180. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 180  AVA definition AVA Early Termination (EaT) takes into account the valuation uncertainty emerging from potential losses that an institution may incur because of the operational risk related to valuation processes. This risk is mainly related, but not limited, to the balance sheet substantiation process and to possible legal disputes (RTS art. 17.1). The main driver for AVA OpR is the operational risk framework adopted by the Institution. Institutions adopting the Advanced Measurement Approach (AMA) Operational Risk defined in the CRR, title III, ch. 4, art. 321-324 (AMA Institutions) are allowed a lighter AVA OpR, as described below. This facilitation is intended to avoid double counting of capital reserves related to the same source of risk. In all other cases (non-AMA Institutions), the AVA OpR is given by 10% of the sum of AVA MPU and AVA CoCo, which can result in high figures. In particular, FAQ 39, remarks that Institutions using the Standardized Method for Operational Risk defined in the CRR, title III, ch. 3, art. 317-320, cannot show that they already take into account the operational risk related to valuation processes. Thus they are not allowed to calculate AVA OpR as AMA institutions. .  AVA main references o EBA RTS, article 17. o EBA FAQs 39, 40, 42. 4: AVA calculation AVA Operational Risk (OpR) [1]
  181. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 181  AVA scope of application Within the general prudent valuation scope (see before), AVA OpR regards in particular those positions that: o can be considered subject to operational risk during the valuation process; o for which in the balance sheet there are provisions for operational risk. Evidences of operational risk related to valuation process are the inclusion of those valuation processes as part of the AMA accounting for the mispricing, misselling and the process execution errors. Furthermore, an AMA usually accounts provision for legal disputes with clients where the underlying of the contract is a fair value position.  AVA Fair Value The fair values of positions under AVA OpR typically does not include any component or adjustment related to operational risk, since these factors do not concur to an exit price. From a risk management point of view, expected operational risk losses may be evaluated using scenario analysis and historical data related to realized operational risk losses. 4: AVA calculation AVA Operational Risk (OpR) [2]
  182. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 182 4: AVA calculation AVA Operational Risk (OpR) [3] AVA Early Termination (ET) (EBA RTS, article 17) reflects the reflects the valuation uncertainty arising from potential losses that may be incurred as a result of operational risk related to valuation processes. Identify valuation positions , = 1, … , , judged to be at-risk during the balance sheet substantiation process, including those due to legal disputes. Compute individual APVA OpR according to the formula , = 10% × , + , Is the AMA (Advanced Measurement Approach) applied to Operational Risk (as defined in Title III Chapter 4 of Regulation (EU) No 575/2013) for valuation positions ? Is there evidence that the operational risk relating to valuation processes of valuation positions is fully accounted for by the AMA calculation ? YES NO , = 0 NO YES Compute total category level AVA OpR = ෍ =1 ,
  183. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 183 Summary 5. Prudent valuation framework o Implementation o Methodological framework o Operational framework o IT framework o Documentation & reporting o Example of prudent valuation framework
  184. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 184 5: Prudent valuation framework Areas: overview Governance Methodology Technology Documentation and reporting Institution
  185. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 185 5: Prudent valuation framework Areas: governance  Define Prudent Valuation processes and controls throughout the operative chain  Apply Indipendent Price Verification (IPV) processes  Guarantee effective controls to govern all fair valued positions  Implement controls to ensure robust evaluation processes even in stressed situations  Design reports for Senior Management (information, frequency and recipients)  Deliver an exhaustive information set to guarantee an appropriate understanding of the valuation uncertainty of the assets and liabilities portfolio. Implement the governance area in terms of roles, responsabilities and processes for measurement, management and control. Governance
  186. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 186 5: Prudent valuation framework Areas: methodology  Design AVA calculation methodologies and aggregation rules  Define scope at single legal entity level and consolidated level  Design, realisation and maintenance of a prudent valuation policy, subject to senior management approval and revision. Define robust methodologies to estimate and aggregate prudent values at banking group level and consolidated level. Methodology
  187. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 187 5: Prudent valuation framework Areas: documentation and reporting  Production chain of prudent values (AVAs)  Match calculation schedule with regulatory deadlines  Deliver AVAs for internal and external reporting Integrate prudent valuations (AVAs) calculation into the management and regulatory reporting processes. Documentation and reporting
  188. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 188 5: Prudent valuation framework Areas: technology  Integration with accounting repositories to determine the prudent valuation scope  Implementation of feeds and calculation engine  Integration with regulatory reporting platform  Monitoring and control input/output data  Development management reporting tools Design and implement an automatic IT chain for feeding and calculation processes of prudent values Technology
  189. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 189 5: Prudent valuation framework Example of Prudent Valuation framework [1/4] Scope Calculation Reporting  Identify fair value positions  Apply exlusionsprovided by the regulator: o Positions subject to prudential filters such that fiar value variations has no or partial impact on CET1 (es. AFS) o Hedge Accounting positions o Back to back positions  Monitor of output data quality Data mining Legal entities scope Prudent Valuation scope Prudent valuation scope Accounting systems
  190. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 190 Scope Calculation Reporting  Identifiy uncertainty levels  Retrieval information from market operators  Retrieval Markit information Data mining Front office systems External sources Uncertainty levels 5: Prudent valuation framework Example of Prudent Valuation framework [2/4]
  191. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 191 Scope Calculation Reporting Check the threshold for core approach (EUR15 bn)  If > = EUR15 bn : o Apply association rules between each single trade and the corresponding AVAs o Apply netting rules o Aggregation and association of uncertainty levels with single trades and AVAs o Apply core AVA calculation rules  if < EUR15bn: o 0,1% Prudent Valuation scope fair value Data mining Prudent Value calculation Prudent valuation scope Uncertainty levels Methodology 5: Prudent valuation framework Example of Prudent Valuation framework [3/4]
  192. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 192 Custom reporting Scope Calculation Reporting  Prepare management reporting  Prepare regulatory reporting (quarterly)  Transmit information to each stakeholder inside the bank Data mining Methodology Management reporting Regulatory reporting 5: Prudent valuation framework Example of Prudent Valuation framework [4/4]
  193. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 193 6: Conclusions Hot topics (1/2)  The CRR is in place since 1st Jan. 2014, and EBA RTS are in the final phase of approval, so prudent valuation is mandatory.  AVA calculation for all fair value positions under the core approach is resource intensive.  The practical application of the EBA RTS requires a lot of expert judgment, in particular to achieve the required 90% level of certainty in the prudent value.  P&L variance test for AVA market price uncertainty and close out costs is rather difficult and controversial.  AVA Investing & Funding cost is a “prudent version” of the FVA, so banks still not accounting FVA in their balance sheets should account the full FVA in the prudent valuation, with the benefit of the diversification factor 0.5. Banks already accounting FVA must calculate a prudent FVA. .  Other XVAs, i.e. MVA (Margin Valuation Adjustment), and KVA (Capital Valuation Adjustment) are controversial. Rule of thumb could be “no fair value accounting, no prudent value capital”.
  194. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 194 6: Conclusions Hot topics (2/2)  Unclear how to manage exclusions for back to back and hedge accounting positions. Is it referred to both Cash Flow Hedge (for which prudential filter is applied) and Fair Value Hedge ?  AVAs have to be deducted from CET1. Hence, possible double counting w.r.t. other capital deductions should be considered, e.g. expected loss amounts (CRR, art. 158- 159), day one profits, etc.  Possible uneven playing field between institutions subject or not to the EU prudent valuation rules.  New regulation and lack of standard market practices allows for widely different applications of the same rules across different institutions. It is reasonable to expect follow ups from Regulators.
  195. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 195 6: Conclusions Questions & Answers
  196. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 196 7: Selected References Regulations [1] 1) BCBS, “International Convergence of Capital Measurement and Capital Standards – A revised framework”, June 2004, http://www.bis.org/publ/bcbs107.htm 2) BCBS, “Revision of the Basel II market risk framework”, July 2009, http://www.bis.org/publ/bcbs158.htm 3) Financial Services Authority, “Dear CEO Letter: Valuation and Product Control”, August 2008, http://www.fsa.gov.uk/pubs/ceo/valuation.pdf 4) Financial Services Authority, “Product Control Findings and Prudent Valuation Presentation”, November 2010, http://www.fsa.gov.uk/pubs/other/pcfindings.pdf 5) Financial Services Authority, “Regulatory Prudent Valuation Return”, Policy Statement 12/7, April 2012, http://www.fsa.gov.uk/library/policy/policy/2012/12-07.shtml 6) International Accounting Standards Board, «International Financial Reporting Standards 13 – Fair Value Measurment», 1° Jan. 2013, www.ifrs.org 7) Regulation EU N.575/2013 of the European Parliament and of the Council on prudential requirements for credit institutions and investment firms and amending Regulation EU N.648/2012, 26 June 2013 8) European Banking Authority, “Discussion Paper relating to Draft Regulatory Technical Standards on prudent valuation under Article 100 of the draft Capital Requirement Regulation (CRR)” EBA/DP/2012/03, 13 November 2012, http://www.eba.europa.eu/-/eba- discussion-paper-on-draft-regulatory-standards-on-prudent-valuation.
  197. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 197 7: Selected References Regulations [2] 9) European Banking Authority, “Consultation Paper Draft Regulatory Technical Standards on prudent valuation under Article 105(34) of Regulation (EU) 575/2013 (Capital Requirements Regulation – CRR)”, EBA/CP/2013/28, 10 July 2013, http://www.eba.europa.eu/regulation-and-policy/market-risk/draft- regulatory-technical-standards-on-prudent-valuation. 10) European Banking Authority, “Questions and Answers on prudent valuation”, October 2013, http://www.eba.europa.eu/-/revised-faqs-on-prudent-valuation-q-1. 11) European Banking Authority, “Quantitative Impact Study on prudent valuation”, November 2013, http://www.eba.europa.eu/-/eba-launches-qis-exercise-on-prudent- valuation. 12) Bank of Italy, Circolare 285, “Disposizioni di vigilanza per le banche”, 17 December 2013, https://www.bancaditalia.it/compiti/vigilanza/normativa/archivio- norme/circolari/c285/index.html 13) European Banking Authority, “EBA final draft Regulatory Technical Standards Regulatory Technical Standards on prudent valuation under Article 105(14) of Regulation (EU) 575/2013 (Capital Requirements Regulation – CRR)”, 31 March 2014, https://www.eba.europa.eu/regulation-and-policy/market-risk/draft- regulatory-technical-standards-on-prudent-valuation
  198. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 198 7: Selected References Regulations [3] 14) European Banking Authority, “EBA final draft Regulatory Technical Standards Regulatory Technical Standards on prudent valuation under Article 105(14) of Regulation (EU) 575/2013 (Capital Requirements Regulation – CRR)”, rev1, 23 January 2015, https://www.eba.europa.eu/regulation-and-policy/market-risk/draft- regulatory-technical-standards-on-prudent-valuation 15) European Commission, Commission delegated regulation (EU) 2016/101, supplementing Regulation (EU) No 575/2013 of the European Parliament and of the Council with regard to regulatory technical standards for prudent valuation under Article 105 (14), 26 Oct. 2015, http://ec.europa.eu/transparency/regdoc/rep/3/2015/EN/3-2015-7245- EN-F1-1.PDF 16) European Banking Authority, Consultation Paper, “Draft Implementing Technical Standards amending Commission Implementing Regulation (EU) 680/2014 on supervisory reporting of institutions”, 4 March 2016, https://www.eba.europa.eu/-/eba-seeks-comments- on-reporting-of-prudent-valuation-information 17) BCBS Consultative Document, “Pillar 3 disclosure requirements – consolidated and enhanced framework”, March 2016, issued for comment by 10 June 2016, http://www.bis.org/bcbs/publ/d356.htm
  199. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 199 7: Selected References Papers 1) Richard Roll, “A simple implicit measure of the effective bid-ask spread in an efficient market”, The Journal of Finance, Vol. XXXIX, n. 4, Sept. 1984. 2) E. Derman, "Model Risk", Goldman Sachs Quantitative Strategies Research Notes, Apr. 1996. 3) R. Rebonato, "Theory and Practice of Model Risk Management”, Quantitative Research Centre (QUARC) of the Royal Bank of Scotland, 2002. 4) R. Cont, "Model uncertainty and its impact on the pricing of derivative instruments", Mathematical Finance, Vol. 16, No. 3, July 2006, 519–547. 5) R. Brar, “A Regulatory Perspective on Prudent Valuation and Best Practice in Product Control”, in “Managing Illiquid Assets”, E. Takagawa editor, Risk Books, 2012. 6) Tanguy Dehapiot, “Prudent Value”, Risk Minds presentation, Dec. 2014.
  200. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 200 7: Selected References Others 1) Ernst & Young, “Prudent Valuation”, 24 May 2013. 2) Ernst & Young, “BIS III – Prudent Valuation – AVAs Overview and relations to IFRS13”, July 2013. 3) Deloitte, “Prudent Valuation”, August 2013, http://www.deloitte.com/assets/Dcom- Belgium/Local%20Assets/Documents/EN/Insights/FSI/be-fsi- prudentvaluation_ebaconsultationpaper_aug2013.pdf. 4) Financial Machineries, http://www.financial-machineries.com. 5) AIFIRM, Associazione Italiana Financial Industry Risk Managers, “Prudent Valuation - Guidelines and sound practices“, Mar. 2016, http://www.aifirm.it/position- paper-prudent-valuation
  201. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 201  10 Dec. 2014: Risk Minds Conference, joint talk on prudent valuation with T. Dehapiot.  28 May 2014: London Stock Exchange, Milano, prudent valuation course, M. Bianchetti, U. Cherubini, E&Y.  16 May 2014: ABI conference, Roma, talk “Funding Valuation and Prudent Valuation Adjustments (PVA & FVA)”, M. Bianchetti, U. Cherubini  24 Sept. 2014: corso ABI, Milano, talk “Prudent valuation“, M. Bianchetti, P. Virgili.  12 Nov. 2014: webinar Numerix, “Prudent Valuation: Bridging the Gap Between Pricing & Risk Management”, M. Bianchetti (link).  24 Nov. 2014: London Stock Exchange, Milano, prudent valuation course, M. Bianchetti, U. Cherubini, E&Y.  10 Dec. 2014: Risk Minds, Amsterdam, talk “Prudent Valuation - Bridging Pricing And Risk Management”, M. Bianchetti (link).  25 Mar. 2015: WBS 4th CVA conference, London, corso “Prudent valuation“, M. Bianchetti, U. Cherubini (link)  May 2015: Global Derivatives, Amsterdam, talk “Prudent Valuation - Bridging Pricing And Risk Management”, M. Bianchetti (link). 7: Selected References Events
  202. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 202  APVA = Additional Prudent Valuation Adjustment  AVA = Additional Valuation Adjustment o MPU = Market Price Uncertainty o CoCo = Close out Costs o MoRi = Model Risk o UCS = Unearned Credit Spread o IFC = Investing and Funding Costs o CoPo = Concentrated Positions o FAC = Future Administrative Costs o EaT = Early Termination o OpR = Operational Risks  CRR = Capital Regulatory Requirements  EBA = European Banking Authority  EU = European Union  FV = Fair Value  FVP = Fair Value Policy  PV = Prudent Value  PVA = Prudent Valuation Adjustment  PVP = Prudent Value Policy  QA = EBA Questions & Answers to DP and QIS  RTS = EBA final draft Regulatory Technical Standards 8: Glossary
  203. M. Bianchetti - Prudent Valuation – Global Derivatives – Budapest,

    10 May 2016 p. 203 Disclaimer and acknowledgments Disclaimer The views and the opinions expressed here are those of the author and do not represent the opinions of his employer. They are not responsible for any use that may be made of these contents. No part of this presentation is intended to influence investment decisions or promote any product or service. Acknowledgments The authors gratefully acknowledges o E. Maffi, S. Vasconi, F. Bertolini, M. Benvenuti, A. Pignataro, S. Vella from E&Y for their contribution to develop the prudent valuation framework and some data analysis. o I. Faerman from Numerix for his contribution for model risk examples. o T. Dehapiot for sharing information and experties on the subject. o Members of the AIFIRM committee on market risk for the stimulating discussions on prudent valuation methodology and applications. o Many other colleagues in Front Office and Risk Management of Intesa Sanpaolo for creating a fertile environment to grow the seeds of prudent valuation.